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666,262,453B
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A359701
a(n) = Sum_{d|n} d^(d + n/d - 2).
[ "1", "3", "10", "69", "626", "7812", "117650", "2097425", "43046803", "1000003158", "25937424602", "743008418676", "23298085122482", "793714774077816", "29192926025406980", "1152921504623628545", "48661191875666868482", "2185911559739084235093", "104127350297911241532842" ]
[ "nonn" ]
16
1
2
[ "A082245", "A124923", "A262843", "A294956", "A359701" ]
null
Seiichi Manyama, Jan 11 2023
2023-08-14T02:00:14
oeisdata/seq/A359/A359701.seq
c56bb571faf12e19d024cf847f6452be
A359702
Odd primes p that are not congruent to 2*k modulo prime(k+1) for any positive integer k.
[ "3", "7", "31", "37", "43", "61", "67", "73", "157", "211", "271", "277", "331", "367", "421", "457", "571", "691", "823", "883", "997", "1093", "1201", "1237", "1303", "1657", "1783", "2053", "2287", "2347", "2371", "2377", "2557", "2803", "2971", "3001", "3061", "3067", "3307", "3313", "3391", "3967", "4021", "4231", "4273", "4357", "4447", "4561", "4603" ]
[ "nonn" ]
24
1
1
[ "A000668", "A019434", "A359702" ]
null
Andrea La Rosa, Jan 11 2023
2023-02-08T00:00:28
oeisdata/seq/A359/A359702.seq
9213bfb43a6080c582a35bb4c2f4b91a
A359703
Number of fillomino dissections of a 2 X n rectangle.
[ "1", "1", "5", "33", "138", "715", "3524", "17119", "84655", "416723", "2047650", "10072806", "49542408", "243701785", "1198732022", "5895900754", "28999718642", "142641530115", "701610208573", "3450988507136", "16974245195432", "83490673950264", "410663317558386", "2019918477187441", "9935315439670326" ]
[ "nonn" ]
36
0
3
[ "A003242", "A359703" ]
null
Don Knuth, Jan 11 2023
2023-01-18T10:34:40
oeisdata/seq/A359/A359703.seq
800f1ad8f214b2985486383ef0a81ba6
A359704
Minimum number of spanning trees in a 3-connected graph on n nodes.
[ "16", "45", "75", "209", "336", "928", "1445", "3965", "6000", "16555" ]
[ "nonn", "more" ]
22
4
1
[ "A006290", "A199676", "A359704" ]
null
David Kofoed Wind, Jan 11 2023
2023-02-17T22:28:52
oeisdata/seq/A359/A359704.seq
88804f1a2a3be4434861688d13c19dc7
A359705
Cogrowth sequence of the Brin-Navas group B.
[ "1", "4", "28", "232", "2092", "19864", "195352", "1970896", "20275692", "211825600", "2240855128", "23952786400", "258287602744", "2806152315048", "30686462795856", "337490492639512", "3730522624066540", "41422293291178872", "461802091590831904", "5167329622166765872" ]
[ "nonn", "walk" ]
13
0
2
null
null
Andrew Elvey Price, Jan 11 2023
2023-01-14T09:39:49
oeisdata/seq/A359/A359705.seq
b70fcc9680679d0147ac3046631c012b
A359706
Number of free (2-sided) ouroboros polyominoes with k=2n cells.
[ "0", "1", "0", "1", "1", "4", "7", "31", "95", "420", "1682", "7544", "33288", "152022", "696096", "3231001" ]
[ "nonn", "more" ]
16
1
6
[ "A002013", "A359706", "A359707" ]
null
Arthur O'Dwyer, Jan 11 2023
2023-01-18T09:36:15
oeisdata/seq/A359/A359706.seq
f4b501cc0b1ad2e30934b03c374be46b
A359707
Number of 1-sided ouroboros polyominoes with k=2n cells.
[ "0", "1", "0", "1", "1", "4", "11", "45", "178", "762", "3309", "14725", "66323", "302342", "1391008", "6453950" ]
[ "nonn", "more" ]
12
1
6
[ "A151514", "A359706", "A359707" ]
null
Arthur O'Dwyer, Jan 11 2023
2023-01-18T09:36:27
oeisdata/seq/A359/A359707.seq
b74b631ae2d8cdb1c48d9bd13df2f4c6
A359708
a(n) is the greatest divisor d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.
[ "1", "2", "1", "4", "5", "3", "1", "8", "9", "10", "1", "6", "1", "2", "1", "16", "17", "18", "1", "20", "21", "2", "1", "12", "5", "2", "9", "7", "1", "3", "1", "32", "33", "34", "1", "36", "37", "19", "1", "40", "41", "42", "1", "4", "5", "2", "1", "24", "1", "25", "17", "4", "1", "18", "1", "14", "1", "2", "1", "6", "1", "2", "1", "64", "65", "66", "1", "68", "69", "35", "1", "72", "73", "74", "1", "38", "1" ]
[ "nonn", "base" ]
13
1
2
[ "A003714", "A359627", "A359708" ]
null
Rémy Sigrist, Jan 12 2023
2023-01-14T08:46:22
oeisdata/seq/A359/A359708.seq
091c12cbd63f31c94ea8959fa46cdee9
A359709
Number of n-step self-avoiding walks on a 2D square lattice whose end-to-end distance is an integer.
[ "1", "4", "4", "12", "28", "76", "164", "732", "1044", "4924", "6724", "30636", "43972", "190516", "313996", "1197908", "2284260", "7678188", "16257604", "50524252", "113052396", "341811828", "773714436", "2358452388", "5245994292", "16447462492", "35395532236", "115129727188", "238542983748", "804980005276" ]
[ "nonn", "walk" ]
27
0
2
[ "A001411", "A103606", "A173380", "A337353", "A356617", "A358036", "A358046", "A359073", "A359709", "A359741" ]
null
Scott R. Shannon, Jan 12 2023
2023-01-15T15:11:35
oeisdata/seq/A359/A359709.seq
6222aa47f705e2caeca4002d921ad20b
A359710
Order of shifts of Thue-Morse sequence.
[ "0", "1", "3", "0", "2", "1", "5", "3", "6", "0", "4", "2", "7", "1", "9", "5", "15", "3", "10", "6", "12", "0", "8", "4", "14", "2", "11", "7", "13", "1", "17", "9", "29", "5", "23", "15", "27", "3", "18", "10", "30", "6", "20", "12", "24", "0", "16", "8", "28", "4", "22", "14", "26", "2", "19", "11", "31", "7", "21", "13", "25", "1", "33", "17", "57", "9", "45", "29", "53", "5", "39", "23", "63", "15" ]
[ "nonn" ]
8
1
3
[ "A010060", "A359710" ]
null
Jeffrey Shallit, Jan 11 2023
2023-01-12T01:42:55
oeisdata/seq/A359/A359710.seq
69a2217b81c3e2388bede4e632b234cc
A359711
a(n) = coefficient of x^n in A(x) such that 1 = Sum_{n=-oo..+oo} (-x)^n * (A(x) + x^(n-1))^(n+1).
[ "1", "3", "11", "42", "165", "671", "2795", "11877", "51286", "224413", "992924", "4434833", "19969030", "90550829", "413148619", "1895338362", "8737219074", "40452543831", "188025758635", "877055405522", "4104269624748", "19262955163275", "90652992751518", "427681283728070", "2022341915324936", "9583224591208298" ]
[ "nonn" ]
29
0
2
[ "A359670", "A359711", "A359712", "A359713", "A363104", "A363105", "A363142", "A363143", "A363144" ]
null
Paul D. Hanna, Jan 17 2023
2023-05-22T02:14:54
oeisdata/seq/A359/A359711.seq
9df2f9a325ceed6551d09e736f48df06
A359712
a(n) = coefficient of x^n in A(x) such that 2 = Sum_{n=-oo..+oo} (-x)^n * (2*A(x) + x^(n-1))^(n+1).
[ "1", "4", "20", "106", "586", "3356", "19728", "118382", "722208", "4466050", "27931600", "176371300", "1122867012", "7199842666", "46454345844", "301384205640", "1964899532794", "12866563846920", "84585757496444", "558060746899684", "3693810227983576", "24521903234307786", "163234951757526400" ]
[ "nonn" ]
20
0
2
[ "A359670", "A359711", "A359712", "A359713", "A361778", "A363104", "A363105" ]
null
Paul D. Hanna, Jan 17 2023
2023-05-22T02:15:14
oeisdata/seq/A359/A359712.seq
ea24c6f6ccd10a2cc675c4e4983fe800
A359713
a(n) = coefficient of x^n in A(x) such that 3 = Sum_{n=-oo..+oo} (-x)^n * (3*A(x) + x^(n-1))^(n+1).
[ "1", "5", "31", "206", "1433", "10329", "76459", "577855", "4440538", "34591555", "272545144", "2168118299", "17390330046", "140486973983", "1142036572271", "9335129425718", "76681549612006", "632655728172281", "5240339959916895", "43561574812700958", "363294379940353624", "3038799803831856805" ]
[ "nonn" ]
12
0
2
[ "A359670", "A359711", "A359712", "A359713", "A363104", "A363105" ]
null
Paul D. Hanna, Jan 17 2023
2023-05-22T02:15:30
oeisdata/seq/A359/A359713.seq
fe77b56fbec2e51c74c44bbe13542b67
A359714
Central terms of triangle A359670; a(n) = A359670(2*n,n) for n >= 0.
[ "1", "6", "68", "970", "15627", "271698", "4980320", "94919382", "1864060550", "37486601966", "768542230128", "16010270917186", "338044149765168", "7220000851821450", "155743662496011552", "3388779105788095886", "74299386925266352272", "1640069094618726916032", "36421678762652448251540" ]
[ "nonn" ]
7
0
2
[ "A359670", "A359714" ]
null
Paul D. Hanna, Jan 17 2023
2023-01-18T14:53:42
oeisdata/seq/A359/A359714.seq
90670b7ed5f81560b843d50380a5d085
A359715
Column 2 of triangle A359670; a(n) = A359670(n+2,2) for n >= 0.
[ "1", "12", "68", "284", "998", "3092", "8724", "22904", "56679", "133516", "301664", "657368", "1387854", "2849168", "5704476", "11166464", "21415632", "40312176", "74593476", "135864792", "243872632", "431835140", "755039948", "1304589104", "2229192801", "3769452152", "6311385252", "10469412968", "17214152072" ]
[ "nonn" ]
5
0
2
[ "A359670", "A359715" ]
null
Paul D. Hanna, Jan 17 2023
2023-01-18T14:54:22
oeisdata/seq/A359/A359715.seq
f97ccc40f45d16e711b2a3e214c2b5d2
A359716
Central terms of triangle A236961: a(n) = A236961(2*n,n) for n >= 0.
[ "1", "2", "21", "412", "12045", "471666", "23248400", "1384919040", "96891179337", "7793576690170", "709024597553360", "72011978446738452", "8079309076956842530", "992583434486548102576", "132551565601036631863350", "19120614257204406476219136", "2963248125855567894279025917", "491063205808744535843792510886" ]
[ "nonn" ]
10
0
2
[ "A236960", "A236961", "A359716" ]
null
Paul D. Hanna, Jan 15 2023
2023-01-17T09:58:25
oeisdata/seq/A359/A359716.seq
999cb6909a7575d7edac165c7815a289
A359717
Row sums of triangle A236961.
[ "1", "2", "7", "42", "376", "4458", "65397", "1140417", "23021210", "527739626", "13539127840", "384262459699", "11952683436071", "404329660018435", "14777538816404041", "580286020131192211", "24364714949633126567", "1089258665667224399708", "51658296648076559411788", "2590348228951371235924053" ]
[ "nonn" ]
8
0
2
[ "A236960", "A236961", "A359717" ]
null
Paul D. Hanna, Jan 15 2023
2023-01-16T11:17:03
oeisdata/seq/A359/A359717.seq
5e46ef992acac3805c33b55bd200e498
A359718
Column 3 of triangle A359670; a(n) = A359670(n+3,3) for n >= 0.
[ "1", "20", "170", "970", "4410", "17172", "59545", "188700", "556085", "1542640", "4065868", "10253720", "24880705", "58351000", "132750390", "293867786", "634623035", "1339924290", "2771178885", "5623152080", "11211087225", "21989506510", "42478375740", "80897833810", "152022961870", "282119268256", "517394696690" ]
[ "nonn" ]
5
0
2
[ "A359670", "A359718" ]
null
Paul D. Hanna, Jan 17 2023
2023-01-18T14:54:27
oeisdata/seq/A359/A359718.seq
cb9fb0361b876a0992cfd465521d701f
A359719
a(n) = coefficient of x^n/n! in A(x) = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (exp(3*n*x) - exp(-(3*n+1)*x)).
[ "1", "-11", "58", "-225", "2146", "-14821", "85590", "-1974433", "9180658", "2927259", "-85838114", "63964584095", "-520091681238", "16934937109019", "-384678052715594", "5238404820228159", "-295855770548974622", "4600244140822151099", "-186350295911412573810", "4851711966859680480959" ]
[ "sign" ]
14
1
2
[ "A359719", "A359919", "A359920" ]
null
Paul D. Hanna, Jan 22 2023
2024-01-05T17:17:22
oeisdata/seq/A359/A359719.seq
c47abdc5addb9cbb9bcb8fbfd6e215c3
A359720
T(n,k) = coefficient of x^n*y^k in A(x,y) such that: x = Sum_{n=-oo..+oo} (-1)^n * x^n * (y + x^n)^n * A(x,y)^n.
[ "1", "1", "1", "2", "4", "5", "1", "7", "21", "9", "20", "51", "49", "7", "43", "170", "179", "66", "2", "110", "454", "711", "381", "54", "262", "1367", "2390", "1894", "523", "25", "674", "3776", "8361", "8070", "3496", "469", "5", "1684", "11062", "27082", "33093", "19129", "4602", "269", "4397", "31054", "89389", "125983", "93908", "33211", "4325", "91", "11320", "89935", "283170", "470439", "421762", "200449", "43062", "2846", "14" ]
[ "nonn", "tabf" ]
9
0
4
[ "A000108", "A097613", "A355357", "A357797", "A359720", "A359721", "A359722", "A359723", "A359724", "A359725", "A359726" ]
null
Paul D. Hanna, Jan 13 2023
2023-01-14T10:53:33
oeisdata/seq/A359/A359720.seq
2610edd04dd029b96f0ef5a5a8c1c67a
A359721
a(n) = coefficient of x^n in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)^n * x^n * (1 + x^n)^n * A(x)^n.
[ "1", "1", "3", "10", "37", "127", "460", "1710", "6461", "24851", "96921", "382358", "1522997", "6116518", "24740564", "100698617", "412126133", "1694982357", "7001729420", "29037602898", "120856092153", "504647152650", "2113469775619", "8875358529059", "37364827472930", "157668052571948", "666735804080597", "2825054673048981" ]
[ "nonn" ]
14
0
3
[ "A355357", "A357797", "A359720", "A359721", "A359723", "A359724" ]
null
Paul D. Hanna, Jan 11 2023
2023-03-14T04:44:06
oeisdata/seq/A359/A359721.seq
e347cfe889a504e5a9404976c825485c
A359722
a(n) = A359720(3*n+1,2*n) for n >= 0.
[ "1", "9", "54", "269", "1254", "5642", "24828", "107613", "461318", "1961102", "8282196", "34792914", "145527004", "606473844", "2519619640", "10440010845", "43158028230", "178049440230", "733229991780", "3014712182790", "12377406450420", "50751988872780", "207859022097480", "850399040956530", "3475797671194524" ]
[ "nonn" ]
5
0
2
[ "A000108", "A359720", "A359722" ]
null
Paul D. Hanna, Jan 14 2023
2023-01-14T10:51:45
oeisdata/seq/A359/A359722.seq
ecd2f2e0ef74257befa8ddbf1fd653f7
A359723
a(n) = coefficient of x^n in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)^n * x^n * (3 + x^n)^n * A(x)^n.
[ "1", "1", "7", "28", "151", "803", "4108", "22532", "125449", "705929", "4035955", "23332364", "136111591", "800561116", "4741777880", "28258286033", "169322163149", "1019483819757", "6164900341534", "37425357962592", "228002416106605", "1393503512669230", "8541839907812651", "52500559705299795", "323483846045526418" ]
[ "nonn" ]
8
0
3
[ "A355357", "A357797", "A359720", "A359721", "A359723", "A359724" ]
null
Paul D. Hanna, Jan 11 2023
2023-01-14T10:08:08
oeisdata/seq/A359/A359723.seq
26a1f07435f194ac94f11f92c6457019
A359724
a(n) = coefficient of x^n in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)^n * x^n * (4 + x^n)^n * A(x)^n.
[ "1", "1", "9", "40", "235", "1456", "8323", "51510", "324674", "2061746", "13308492", "86876405", "572169044", "3799139674", "25403610485", "170901457100", "1155976005944", "7856772779823", "53630378512469", "367507023955203", "2527254094342404", "17435029150904202", "120633291776867632", "836907189915348056" ]
[ "nonn" ]
6
0
3
[ "A355357", "A357797", "A359720", "A359721", "A359723", "A359724" ]
null
Paul D. Hanna, Jan 11 2023
2023-01-14T10:08:52
oeisdata/seq/A359/A359724.seq
78f5978bfb8fc41d6b0261ea62f55b56
A359725
a(n) = A359720(n+2,1), for n >= 0.
[ "2", "5", "21", "51", "170", "454", "1367", "3776", "11062", "31054", "89935", "254654", "733725", "2088612", "6004175", "17150397", "49267851", "141065942", "405274932", "1162440833", "3341173303", "9596468129", "27600014912", "79359955225", "228397685542", "657335642733", "1893081845674", "5452722985712" ]
[ "nonn" ]
7
0
1
[ "A355357", "A359720", "A359725", "A359726" ]
null
Paul D. Hanna, Jan 14 2023
2023-01-14T10:51:50
oeisdata/seq/A359/A359725.seq
58d37a16816e35d284e44a48833fc67d
A359726
a(n) = A359720(n+3,2), for n >= 0.
[ "1", "9", "49", "179", "711", "2390", "8361", "27082", "89389", "283170", "905307", "2825245", "8854116", "27341969", "84550769", "259046260", "793589833", "2416512240", "7352490113", "22279068811", "67435591018", "203525629398", "613550161717", "1845654390776", "5545861291941", "16637001197044", "49858191850323" ]
[ "nonn" ]
5
0
2
[ "A355357", "A359720", "A359725", "A359726" ]
null
Paul D. Hanna, Jan 14 2023
2023-01-14T10:51:54
oeisdata/seq/A359/A359726.seq
7b4387e5699567acafdc07f6afecfcfb
A359727
Beattific 'primes': numbers n > 1 not equal to floor(k*m*phi) or floor(k*m*phi^2) for any smaller element k in this sequence and any positive integer m.
[ "2", "4", "7", "8", "13", "14", "17", "23", "24", "28", "30", "39", "40", "43", "46", "49", "50", "53", "59", "65", "66", "70", "72", "75", "76", "81", "86", "88", "92", "96", "98", "107", "108", "114", "117", "118", "123", "127", "134", "140", "143", "144", "149", "150", "153", "156", "159", "160", "163", "166", "175", "176", "179", "182", "185", "191", "195" ]
[ "nonn" ]
23
1
1
[ "A000201", "A001622", "A001950", "A104457", "A359727" ]
null
James Propp, Jan 11 2023
2023-01-28T13:44:56
oeisdata/seq/A359/A359727.seq
310c0c26791461bef5b47011e715e332
A359728
a(1) = 1; a(n) is the smallest positive number not among the first k terms where k is the number of times a(n-1) has occurred.
[ "1", "2", "2", "3", "2", "3", "3", "3", "4", "2", "4", "3", "4", "3", "4", "4", "4", "4", "4", "4", "5", "2", "4", "5", "3", "4", "5", "3", "4", "5", "4", "5", "4", "5", "4", "5", "4", "5", "4", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "5", "6", "2", "4", "5", "6", "3", "5", "6", "3", "5", "6", "4", "5", "6", "4", "5", "6", "4", "6", "4", "6", "4", "6", "5", "6", "5", "6", "5", "6", "5", "6", "5", "6", "5", "6" ]
[ "nonn" ]
25
1
2
[ "A358921", "A359728" ]
null
Neal Gersh Tolunsky, Jan 11 2023
2023-03-13T06:07:54
oeisdata/seq/A359/A359728.seq
00b9e974e074f7566fb720deefb63f33
A359729
The number of Carmichael numbers smaller than the n-th Carmichael number which are quadratic residues of the n-th Carmichael number.
[ "0", "0", "0", "0", "0", "1", "1", "0", "1", "1", "2", "3", "4", "2", "3", "2", "2", "3", "2", "3", "3", "3", "2", "0", "3", "4", "2", "6", "7", "1", "1", "7", "5", "7", "3", "8", "3", "6", "7", "5", "5", "7", "7", "8", "6", "5", "6", "6", "12", "10", "1", "6", "9", "7", "6", "9", "4", "7", "7", "8", "8", "2", "3", "10", "6", "12", "8", "7", "8", "6", "12", "12", "12", "9", "6", "16", "8", "9", "8", "10", "15", "9", "8", "7", "13", "9", "12", "11", "10", "12", "13", "10", "18", "7" ]
[ "nonn" ]
14
1
11
[ "A002997", "A317247", "A359729" ]
null
R. J. Mathar, Jan 12 2023
2023-01-23T09:10:40
oeisdata/seq/A359/A359729.seq
c4fb08b2ba0978ce8ce4c9177a7fb3ba
A359730
a(n) = Sum_{d|n} 2^(d-1) * d^(n/d).
[ "1", "5", "13", "41", "81", "245", "449", "1185", "2413", "5585", "11265", "26693", "53249", "118081", "248733", "535041", "1114113", "2390885", "4980737", "10557201", "22050797", "46265345", "96468993", "201795717", "419480401", "873123841", "1812204685", "3760019521", "7784628225", "16111126325", "33285996545", "68729044993" ]
[ "nonn" ]
13
1
2
[ "A001787", "A308366", "A359700", "A359730" ]
null
Seiichi Manyama, Jan 12 2023
2023-08-14T01:59:37
oeisdata/seq/A359/A359730.seq
6783d4131cb2a6955d858c1887789ab1
A359731
a(n) = (1/2) * Sum_{d|n} (2*d)^d.
[ "1", "9", "109", "2057", "50001", "1493109", "52706753", "2147485705", "99179645293", "5120000050009", "292159150705665", "18260173719523445", "1240576436601868289", "91029559915023973833", "7174453500000000050109", "604462909807316734838793", "54214017802982966177103873" ]
[ "nonn", "easy" ]
21
1
2
[ "A062796", "A076723", "A359731", "A359732" ]
null
Seiichi Manyama, Jan 12 2023
2023-08-14T02:00:18
oeisdata/seq/A359/A359731.seq
61e08d9b92bd9811b68a8aa355c9f6b3
A359732
a(n) = Sum_{d|n} d^(2*d-1).
[ "1", "9", "244", "16393", "1953126", "362797308", "96889010408", "35184372105225", "16677181699666813", "10000000000001953134", "7400249944258160101212", "6624737266949237373933820", "7056410014866816666030739694", "8819763977946281130541873428720" ]
[ "nonn", "easy" ]
15
1
2
[ "A308688", "A308696", "A359731", "A359732" ]
null
Seiichi Manyama, Jan 12 2023
2023-08-14T02:00:25
oeisdata/seq/A359/A359732.seq
e925e083198be6f25d9156602a957b5f
A359733
a(n) = (1/2) * Sum_{d|n} (2*d)^(n/d).
[ "1", "4", "7", "20", "21", "88", "71", "296", "373", "1084", "1035", "5084", "4109", "16496", "20787", "67728", "65553", "286516", "262163", "1070180", "1189937", "4194568", "4194327", "17760824", "16827241", "67109228", "72150655", "269503660", "268435485", "1104603808", "1073741855", "4303389216", "4476371181" ]
[ "nonn", "easy" ]
16
1
2
[ "A055225", "A076717", "A359733" ]
null
Seiichi Manyama, Jan 12 2023
2023-08-14T02:00:21
oeisdata/seq/A359/A359733.seq
4a8711a2263cb31a80c5d690799e76ae
A359734
Lexicographically earliest sequence of distinct nonnegative integers such that the sequence A051699(a(n)) (distance from the nearest prime) has the same sequence of digits.
[ "1", "10", "2", "0", "3", "26", "9", "119", "532", "4", "6", "896", "118", "34", "15", "93", "121", "531", "898", "205", "8", "12", "533", "50", "117", "14", "122", "1078", "56", "16", "21", "18", "144", "64", "20", "895", "1138", "899", "25", "5", "186", "1077", "22", "27", "204", "76", "86", "206", "7", "24", "28", "120", "30", "123", "32", "33", "35", "36", "11", "300" ]
[ "nonn", "base" ]
19
0
2
[ "A000040", "A051699", "A359734", "A359736", "A359737" ]
null
M. F. Hasler and Eric Angelini, Jan 12 2023
2024-12-21T18:22:54
oeisdata/seq/A359/A359734.seq
58130846fa8bfcd1eb37c0ecb1005bf7
A359735
Let f(s,n) = 2^n + s*n, with s in {-1, 1}. Let c be the number of primes out of the pair f(-1,n), f(1,n). If only f(-1,n) is prime, a(n) = -1, otherwise a(n) = c.
[ "0", "1", "-1", "2", "0", "1", "0", "0", "0", "2", "0", "0", "0", "-1", "0", "1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
43
0
4
[ "A006127", "A048744", "A052007", "A129962", "A359735" ]
null
Jean-Marc Rebert, Jan 12 2023
2025-01-18T16:33:52
oeisdata/seq/A359/A359735.seq
01cbf0a7cf5eb22e0d8b74cd4516fab9
A359736
Lexicographically earliest sequence of distinct nonnegative integers such that the sequence d(n) = dist(a(n), SQUARES) has the same sequence of digits.
[ "0", "10", "1", "2", "6", "42", "20", "7", "11", "4", "56", "3", "5", "21", "30", "43", "12", "31", "14", "8", "13", "9", "29", "19", "15", "18", "22", "17", "24", "32", "72", "26", "28", "90", "23", "91", "35", "109", "37", "41", "48", "73", "27", "34", "50", "57", "38", "40", "33", "47", "71", "51", "62", "55", "66", "89", "112", "16", "79", "39", "130", "63", "46", "44", "65", "25", "135" ]
[ "nonn", "base" ]
11
0
2
[ "A000290", "A053188", "A359734", "A359736", "A359737" ]
null
M. F. Hasler and Eric Angelini, Jan 12 2023
2024-12-21T18:20:50
oeisdata/seq/A359/A359736.seq
2e83cde00d80dfde738ae6f67dc1e170
A359737
Lexicographically earliest sequence of distinct nonnegative integers such that the sequence d(n) = A296239(a(n)) has the same sequence of digits, where A296239 gives the distance from the nearest Fibonacci number, cf. A000045.
[ "0", "12", "10", "4", "1", "17", "6", "7", "41", "27", "48", "25", "9", "11", "62", "30", "42", "15", "26", "43", "14", "20", "28", "19", "16", "2", "38", "23", "22", "29", "32", "40", "51", "18", "33", "59", "36", "3", "53", "47", "35", "46", "54", "49", "57", "24", "63", "87", "31", "91", "111", "64", "37", "113", "5", "39", "56", "88", "81", "52", "58", "50", "80", "86", "61", "92", "60", "141", "85", "82", "147" ]
[ "nonn", "base" ]
16
0
2
[ "A000045", "A296239", "A359734", "A359736", "A359737" ]
null
M. F. Hasler and Eric Angelini, Jan 12 2023
2024-12-21T18:24:34
oeisdata/seq/A359/A359737.seq
31e2bf73faadda3de5c65e1d6bc0a4d3
A359738
a(n) = [x^n] (2*x^4 + 2*x^3 + 2*x^2 + x + 1)/(x^2 + 1).
[ "1", "1", "1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1" ]
[ "sign", "easy" ]
27
0
null
[ "A057077", "A087960", "A100615", "A266591", "A359738" ]
null
Peter Luschny, Jan 23 2023
2025-03-25T02:31:34
oeisdata/seq/A359/A359738.seq
c8b394aeafdd2ac29a53557087ddfc6a
A359739
a(n) = Sum_{j=0..n, j even} binomial(n, j) * oddfactorial(j/2) * n^j, where oddfactorial(n) = (2*n)! / (2^n*n!).
[ "1", "1", "5", "28", "865", "9626", "758701", "12606280", "1872570113", "41351249980", "9925656304501", "273345587759696", "96567039881462305", "3185756105692821688", "1555524449985942662045", "59790093545794928817376", "38565845285812075675023361", "1692346747225524397926264080", "1393672439437011815394433559653" ]
[ "nonn" ]
9
0
3
[ "A359739", "A359760" ]
null
Peter Luschny, Jan 12 2023
2023-01-18T09:34:20
oeisdata/seq/A359/A359739.seq
bb7646d7d276654c0793b344a55245f5
A359740
Maximal number of moves needed by a knight to reach every cell from a fixed position on an n X n X n chessboard, or -1 if it is not possible to reach every square.
[ "0", "-1", "-1", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67" ]
[ "sign", "easy" ]
40
1
4
[ "A232007", "A359740" ]
null
Marco Ripà, Jan 12 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359740.seq
c2d3ff2273090c65872d31cb9677a862
A359741
Number of n-step self-avoiding walks on a 3D cubic lattice whose end-to-end distance is an integer.
[ "1", "6", "6", "30", "78", "1134", "1350", "20574", "23238", "390606", "496998", "7614750", "10987926", "152120934", "237122526", "3110708214", "5017927638", "64718847438", "105210653478", "1362453235998" ]
[ "nonn", "walk", "more" ]
16
0
2
[ "A001412", "A118313", "A359133", "A359709", "A359741" ]
null
Scott R. Shannon, Jan 12 2023
2023-01-15T15:11:26
oeisdata/seq/A359/A359741.seq
75a1ae0e4d608ac237767dd167655e8d
A359742
Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives p values.
[ "2", "3", "5", "7", "12", "19", "31", "34", "53", "87", "118", "205", "323", "441", "559", "612", "1171", "1783", "1901", "3684", "4296", "7980", "12276", "16572", "20868", "25164", "29460", "33756", "38052", "39953", "78005", "111761", "151714", "229719", "381433", "533147", "684861", "796622", "948336", "1633197", "2581533", "4214730" ]
[ "nonn", "easy" ]
8
0
1
[ "A359742", "A359743", "A359744" ]
null
Sean A. Irvine, Jan 12 2023
2023-01-13T00:08:04
oeisdata/seq/A359/A359742.seq
e9765fb3f67261da2f0861ff9655349a
A359743
Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives q values.
[ "1", "2", "3", "4", "7", "11", "18", "20", "31", "51", "69", "120", "189", "258", "327", "358", "685", "1043", "1112", "2155", "2513", "4668", "7181", "9694", "12207", "14720", "17233", "19746", "22259", "23371", "45630", "65376", "88747", "134377", "223124", "311871", "400618", "465994", "554741", "955359", "1510100", "2465459", "3975559" ]
[ "nonn", "easy" ]
5
0
2
[ "A359742", "A359743", "A359744" ]
null
Sean A. Irvine, Jan 12 2023
2023-01-12T23:01:27
oeisdata/seq/A359/A359743.seq
2928c0d60bd88f3904ceb231cc848ad4
A359744
Viggo Brun's ternary continued fraction algorithm applied to { log 2, log 3/2, log 5/4 } produces a list of triples (p,q,r); sequence gives r values.
[ "1", "1", "2", "2", "4", "6", "10", "11", "17", "28", "38", "66", "104", "142", "180", "197", "377", "574", "612", "1186", "1383", "2569", "3952", "5335", "6718", "8101", "9484", "10867", "12250", "12862", "25112", "35979", "48841", "73953", "122794", "171635", "220476", "256455", "305296", "525772", "831068", "1356840", "2187908", "3544748" ]
[ "nonn", "easy" ]
5
0
3
[ "A359742", "A359743", "A359744" ]
null
Sean A. Irvine, Jan 12 2023
2023-01-12T23:01:22
oeisdata/seq/A359/A359744.seq
961495ad02d51da2950423cb6e7fcc46
A359745
Numbers k such that k and k+1 have the same ordered prime signature.
[ "2", "14", "21", "33", "34", "38", "44", "57", "85", "86", "93", "94", "116", "118", "122", "133", "135", "141", "142", "145", "158", "171", "177", "201", "202", "205", "213", "214", "217", "218", "230", "253", "285", "296", "298", "301", "302", "326", "332", "334", "381", "387", "393", "394", "429", "434", "445", "446", "453", "481", "501", "514", "526", "537", "542" ]
[ "nonn" ]
10
1
1
[ "A052213", "A124010", "A359745", "A359746" ]
null
Amiram Eldar, Jan 13 2023
2023-01-17T09:23:56
oeisdata/seq/A359/A359745.seq
e6b0ee37784b7d0922e150ffb142f241
A359746
Numbers k such that k, k+1 and k+2 have the same ordered prime signature.
[ "33", "85", "93", "141", "201", "213", "217", "301", "393", "445", "633", "697", "921", "1041", "1137", "1261", "1309", "1345", "1401", "1641", "1761", "1837", "1885", "1893", "1941", "1981", "2013", "2101", "2181", "2217", "2305", "2361", "2433", "2461", "2517", "2641", "2665", "2721", "2733", "3097", "3385", "3601", "3693", "3729", "3865", "3901", "3957" ]
[ "nonn" ]
22
1
1
[ "A039833", "A052214", "A075039", "A124010", "A175590", "A359745", "A359746" ]
null
Amiram Eldar, Jan 13 2023
2023-01-17T09:23:50
oeisdata/seq/A359/A359746.seq
2f288d453675713da5037b0872e5c8ec
A359747
Numbers k such that k*(k+1) has in its canonical prime factorization mutually distinct exponents.
[ "1", "3", "4", "7", "8", "16", "24", "27", "31", "48", "63", "71", "72", "107", "108", "124", "127", "199", "242", "243", "256", "400", "431", "432", "499", "512", "576", "647", "783", "863", "967", "971", "1024", "1151", "1152", "1372", "1567", "1600", "1999", "2187", "2311", "2400", "2591", "2592", "2887", "2916", "3087", "3136", "3456", "3887", "3888", "3968", "4000" ]
[ "nonn" ]
12
1
2
[ "A001694", "A002378", "A060355", "A130091", "A342028", "A359747", "A359748" ]
null
Amiram Eldar, Jan 13 2023
2023-01-17T09:23:42
oeisdata/seq/A359/A359747.seq
a40d91631852f274d413eab1c7badad0
A359748
Numbers k such that k and k+1 are both in A359747.
[ "3", "7", "71", "107", "242", "431", "1151", "2591", "3887", "21599", "49391", "76831", "79999", "107647", "139967", "179999", "197567", "268911", "345599", "346111", "401407", "438047", "472391", "995327", "1031047", "1143071", "1249999", "1254527", "1349999", "1438207", "1685447", "2056751", "2411207", "2829887", "3269807", "4464071" ]
[ "nonn" ]
9
1
1
[ "A130091", "A342028", "A342029", "A359748" ]
null
Amiram Eldar, Jan 13 2023
2023-01-17T08:15:52
oeisdata/seq/A359/A359748.seq
20a1020289722bbdcdb4874d6227f61a
A359749
Numbers k such that k and k+1 do not share a common exponent in their prime factorizations.
[ "1", "3", "4", "7", "8", "9", "15", "16", "24", "25", "26", "27", "31", "32", "35", "36", "48", "63", "64", "71", "72", "81", "100", "107", "108", "120", "121", "124", "125", "127", "128", "143", "144", "168", "169", "195", "196", "199", "200", "215", "216", "224", "225", "242", "243", "255", "256", "287", "289", "323", "342", "361", "391", "392", "399", "400", "431", "432", "440" ]
[ "nonn" ]
11
1
2
[ "A000079", "A000225", "A001694", "A002496", "A049533", "A060355", "A075408", "A078324", "A078325", "A359747", "A359749" ]
null
Amiram Eldar, Jan 13 2023
2023-01-17T09:23:37
oeisdata/seq/A359/A359749.seq
a83815e1cb9e024541b1d8795c29156b
A359750
Numbers that are a product of one or more factorials j!, j >= 2, in at least two ways.
[ "24", "48", "96", "144", "192", "288", "384", "576", "720", "768", "864", "1152", "1440", "1536", "1728", "2304", "2880", "3072", "3456", "4320", "4608", "5184", "5760", "6144", "6912", "8640", "9216", "10368", "11520", "12288", "13824", "17280", "18432", "20736", "23040", "24576", "25920", "27648", "31104", "34560", "36864", "40320", "41472", "46080" ]
[ "nonn" ]
7
1
1
[ "A001013", "A359750" ]
null
David A. Corneth, Jan 13 2023
2023-01-13T07:34:26
oeisdata/seq/A359/A359750.seq
1f2d049b2ccd9f8d1d8ea6d5b93bca21
A359751
Numbers m > 1 such that for all k > 1, m can be written as a product of factorials without using k!.
[ "24", "576", "720", "2880", "13824", "17280", "40320", "69120", "241920", "331776", "362880", "414720", "518400", "725760", "967680", "1451520", "1658880", "2073600", "2903040", "3628800", "5806080", "7962624", "8294400", "8709120", "9953280", "12441600", "14515200", "17418240", "23224320", "29030400", "34836480", "39813120", "43545600" ]
[ "nonn" ]
43
1
1
[ "A001013", "A359750", "A359751" ]
null
David A. Corneth and Peter Munn, Jan 13 2023
2023-01-17T16:31:55
oeisdata/seq/A359/A359751.seq
88b8c5d85eb3f2814a1e370c7b214e13
A359752
Lexicographically earliest array of distinct positive integers read by antidiagonals such that integers in cells which are a knight's move apart are coprime.
[ "1", "2", "3", "4", "5", "7", "6", "8", "9", "11", "13", "17", "19", "23", "10", "12", "15", "21", "27", "16", "14", "22", "25", "29", "31", "37", "20", "33", "18", "24", "35", "26", "39", "41", "43", "47", "49", "53", "59", "61", "32", "55", "67", "45", "28", "30", "51", "57", "63", "34", "36", "71", "73", "38", "44", "40", "65", "79", "83", "89", "85", "77", "91", "69", "42", "75" ]
[ "nonn", "tabl" ]
31
1
2
[ "A097883", "A359752" ]
null
Jodi Spitz, Mar 07 2023
2023-03-10T13:35:19
oeisdata/seq/A359/A359752.seq
7d73730cce756c0e584ddcbe3b7f22f0
A359753
a(n) is the number of subsets of the divisors of k which sum to k+1 where k is a number all of whose prime divisors are consecutive primes starting at 2.
[ "1", "1", "1", "1", "1", "3", "1", "2", "5", "5", "1", "8", "11", "3", "33", "1", "27", "20", "21", "21", "271", "1", "117", "13", "4", "720", "43", "149", "143", "2155", "1", "109", "448", "444", "55", "21963", "85", "19223", "1247", "279", "17073", "5", "1", "15086", "1835", "13732", "13851", "760", "675187", "37", "171", "588", "9558", "73713", "135669", "144", "1", "8206", "7254" ]
[ "nonn" ]
4
1
6
[ "A055932", "A359196", "A359753" ]
null
David A. Corneth, Jan 17 2023
2023-01-28T12:37:13
oeisdata/seq/A359/A359753.seq
293972575fc8ebca83ba1b46c076bf45
A359754
Positions of first appearances in the sequence of weighted sums of reversed prime indices (A318283).
[ "1", "2", "3", "4", "6", "8", "10", "12", "16", "18", "19", "24", "27", "32", "36", "43", "48", "59", "61", "64", "67", "71", "79", "83", "89", "97", "101", "103", "107", "109", "113", "127", "131", "137", "139", "149", "151", "157", "163", "167", "173", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233", "239", "241", "251", "257", "263", "269" ]
[ "nonn" ]
6
1
2
[ "A001222", "A029931", "A053632", "A056239", "A089633", "A112798", "A124757", "A243055", "A296150", "A304818", "A318283", "A320387", "A358136", "A358137", "A358194", "A359361", "A359497", "A359674", "A359675", "A359677", "A359678", "A359679", "A359680", "A359681", "A359682", "A359683", "A359754", "A359755" ]
null
Gus Wiseman, Jan 15 2023
2023-01-16T11:14:59
oeisdata/seq/A359/A359754.seq
774169698c8d75c36ae164403533f928
A359755
Positions of first appearances in the sequence of weighted sums of prime indices (A304818).
[ "1", "2", "3", "4", "6", "7", "8", "10", "12", "15", "16", "18", "20", "24", "26", "28", "36", "40", "46", "48", "50", "52", "56", "62", "68", "74", "76", "86", "88", "92", "94", "106", "107", "118", "122", "124", "131", "134", "136", "142", "146", "152", "158", "164", "166", "173", "178", "188", "193", "194", "199", "202", "206", "214", "218", "226", "229", "236", "239", "254" ]
[ "nonn" ]
6
1
2
[ "A001222", "A029931", "A053632", "A056239", "A089633", "A112798", "A124757", "A243055", "A304818", "A318283", "A320387", "A358136", "A358137", "A358194", "A359361", "A359497", "A359674", "A359675", "A359676", "A359678", "A359679", "A359680", "A359681", "A359682", "A359683", "A359754", "A359755", "A359756" ]
null
Gus Wiseman, Jan 15 2023
2023-01-16T11:15:03
oeisdata/seq/A359/A359755.seq
7abc8fe19c8f7aef3e0a30356370cdc0
A359756
First position of n in the sequence of zero-based weighted sums of standard compositions (A124757), if we start with position 0.
[ "0", "3", "6", "7", "13", "14", "15", "27", "29", "30", "31", "55", "59", "61", "62", "63", "111", "119", "123", "125", "126" ]
[ "nonn", "more" ]
6
0
2
[ "A000120", "A029931", "A053632", "A059893", "A066099", "A070939", "A083329", "A089633", "A124757", "A231204", "A304818", "A318283", "A320387", "A359043", "A359674", "A359676", "A359678", "A359681", "A359682", "A359756" ]
null
Gus Wiseman, Jan 17 2023
2023-01-19T11:10:50
oeisdata/seq/A359/A359756.seq
35e44cfc4ab5837142a97dcc34561a5e
A359757
Greatest positive integer whose weakly increasing prime indices have zero-based weighted sum (A359674) equal to n.
[ "4", "9", "25", "49", "121", "169", "289", "361", "529", "841", "961", "1369", "1681", "1849", "2209", "2809", "3481", "3721", "4489", "5041", "5329", "6241", "6889", "7921", "9409", "10201", "12167", "11449", "15341", "24389", "16399", "26071", "29791", "31117", "35557", "50653", "39401", "56129", "68921", "58867", "72283", "83521", "79007", "86903", "103823" ]
[ "nonn" ]
12
1
1
[ "A001222", "A001248", "A029931", "A053632", "A055932", "A056239", "A089633", "A112798", "A124757", "A231204", "A243055", "A296150", "A304818", "A318283", "A320387", "A358136", "A358137", "A358194", "A359361", "A359497", "A359674", "A359675", "A359676", "A359677", "A359678", "A359679", "A359680", "A359681", "A359682", "A359683", "A359754", "A359755", "A359757" ]
null
Gus Wiseman, Jan 16 2023
2023-01-21T22:27:00
oeisdata/seq/A359/A359757.seq
4ace6c716a10e762ecaef256380b5938
A359758
Expansion of 1/sqrt(1 - 4*x/(1-x)^5).
[ "1", "2", "16", "110", "770", "5512", "40066", "294484", "2182850", "16288430", "122198926", "920820578", "6964483628", "52840433000", "401990254180", "3065365241440", "23422905551018", "179302895759782", "1374785979255880", "10556280995419090", "81161958814162700", "624750086745027388" ]
[ "nonn" ]
24
0
2
[ "A085362", "A110170", "A162478", "A359489", "A359758", "A360132" ]
null
Seiichi Manyama, Mar 24 2023
2023-03-28T14:00:50
oeisdata/seq/A359/A359758.seq
49dfb7f0de7985c0ec55017f42f2845f
A359759
Table read by rows. T(n, k) = (-1)^(n - k) * Sum_{j=k..n} binomial(n, j) * A354794(j, k) * j^(n - j).
[ "1", "0", "1", "0", "-3", "1", "0", "13", "-9", "1", "0", "-103", "79", "-18", "1", "0", "1241", "-905", "265", "-30", "1", "0", "-19691", "13771", "-4290", "665", "-45", "1", "0", "384805", "-262885", "82621", "-14630", "1400", "-63", "1", "0", "-8918351", "6007247", "-1888362", "353381", "-40390", "2618", "-84", "1" ]
[ "sign", "tabl" ]
13
0
5
[ "A048993", "A059297", "A354794", "A357247", "A359759" ]
null
Peter Luschny, Jan 27 2023
2023-01-28T12:17:09
oeisdata/seq/A359/A359759.seq
0cd7f59ba84efaef6cb2f9d116539b7f
A359760
Triangle read by rows. The Kummer triangle, the coefficients of the Kummer polynomials. K(n, k) = binomial(n, k) * oddfactorial(k/2) if k is even, otherwise 0, where oddfactorial(z) := (2*z)!/(2^z*z!).
[ "1", "1", "0", "1", "0", "1", "1", "0", "3", "0", "1", "0", "6", "0", "3", "1", "0", "10", "0", "15", "0", "1", "0", "15", "0", "45", "0", "15", "1", "0", "21", "0", "105", "0", "105", "0", "1", "0", "28", "0", "210", "0", "420", "0", "105", "1", "0", "36", "0", "378", "0", "1260", "0", "945", "0", "1", "0", "45", "0", "630", "0", "3150", "0", "4725", "0", "945", "1", "0", "55", "0", "990", "0", "6930", "0", "17325", "0", "10395", "0" ]
[ "nonn", "tabl" ]
21
0
9
[ "A000085", "A001147", "A001464", "A001879", "A002522", "A005425", "A047974", "A056107", "A066325", "A073278", "A099174", "A100861", "A104556", "A111924", "A115329", "A123022", "A123023", "A144299", "A344501", "A359739", "A359760", "A359761" ]
null
Peter Luschny, Jan 13 2023
2025-04-13T03:33:15
oeisdata/seq/A359/A359760.seq
d85f1fcfa0dd49feb0b46d28e9bcec80
A359761
a(n) = binomial(4*n, 2*n)*(2*n)!/(2^n*n!).
[ "1", "6", "210", "13860", "1351350", "174594420", "28109701620", "5421156741000", "1218404977539750", "312723944235202500", "90252130306279441500", "28929910132721937339000", "10197793321784482911997500", "3920659309406065045704885000", "1632674555274097086889962825000", "732091270584905133761459330730000" ]
[ "nonn", "easy" ]
7
0
2
[ "A359760", "A359761" ]
null
Peter Luschny, Jan 14 2023
2023-01-25T09:13:20
oeisdata/seq/A359/A359761.seq
85f92f49fee3e82070d88e7df5fdfcd6
A359762
Array read by ascending antidiagonals. T(n, k) = n!*[x^n] exp(x + (k/2) * x^2). A generalization of the number of involutions (or of 'telephone numbers').
[ "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "4", "3", "1", "1", "1", "10", "7", "4", "1", "1", "1", "26", "25", "10", "5", "1", "1", "1", "76", "81", "46", "13", "6", "1", "1", "1", "232", "331", "166", "73", "16", "7", "1", "1", "1", "764", "1303", "856", "281", "106", "19", "8", "1", "1", "1", "2620", "5937", "3844", "1741", "426", "145", "22", "9", "1", "1" ]
[ "nonn", "tabl" ]
29
0
8
[ "A000012", "A000027", "A000085", "A016777", "A047974", "A100536", "A115327", "A115329", "A115331", "A277614", "A293720", "A359760", "A359762" ]
null
Peter Luschny, Jan 14 2023
2025-03-25T02:30:26
oeisdata/seq/A359/A359762.seq
dbf4982ac1253746ae53cf45ffac0072
A359763
Dirichlet inverse of A065043, where A065043 is the characteristic function of the numbers with an even number of prime factors (counted with multiplicity).
[ "1", "0", "0", "-1", "0", "-1", "0", "0", "-1", "-1", "0", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "-1", "-1", "0", "1", "-1", "-1", "0", "0", "0", "0", "0", "0", "-1", "-1", "-1", "2", "0", "-1", "-1", "1", "0", "0", "0", "0", "0", "-1", "0", "0", "-1", "0", "-1", "0", "0", "1", "-1", "1", "-1", "-1", "0", "3", "0", "-1", "0", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "-1", "0", "0", "-1", "0", "0", "0", "0", "-1", "0", "3", "-1", "-1", "-1", "1", "0", "3", "-1", "0", "-1", "-1", "-1", "0", "0", "0", "0", "2", "0", "0", "0", "1", "0" ]
[ "sign" ]
19
1
36
[ "A003961", "A008836", "A008966", "A026424", "A028260", "A046523", "A065043", "A066829", "A101296", "A358777", "A359763", "A359764", "A359765", "A359766", "A359767", "A359773", "A359780", "A359823" ]
null
Antti Karttunen, Jan 13 2023
2023-01-14T17:47:06
oeisdata/seq/A359/A359763.seq
ef3010b0f2dd504a2fb27e4a7f778ae9
A359764
Parity of A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity).
[ "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "1", "1", "1", "0", "1", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "1" ]
[ "nonn" ]
15
1
null
[ "A003961", "A030229", "A065043", "A359595", "A359763", "A359764", "A359765", "A359766", "A359767", "A359774", "A359781", "A359791", "A359824" ]
null
Antti Karttunen, Jan 13 2023
2023-01-14T17:47:18
oeisdata/seq/A359/A359764.seq
61e12fd3c71979a2416844396eb7b29a
A359765
Positions of odd terms in A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity).
[ "1", "4", "6", "9", "10", "14", "15", "21", "22", "24", "25", "26", "33", "34", "35", "38", "39", "40", "46", "49", "51", "54", "55", "56", "57", "58", "60", "62", "65", "69", "74", "77", "82", "84", "85", "86", "87", "88", "90", "91", "93", "94", "95", "104", "106", "111", "115", "118", "119", "121", "122", "123", "126", "129", "132", "133", "134", "135", "136", "140", "141", "142", "143", "144", "145", "146", "150", "152", "155", "156" ]
[ "nonn" ]
8
1
2
[ "A028260", "A065043", "A359596", "A359763", "A359764", "A359765", "A359766", "A359767", "A359791" ]
null
Antti Karttunen, Jan 13 2023
2023-01-13T16:25:34
oeisdata/seq/A359/A359765.seq
735a5528d420a81c44a30ea1607b14d1
A359766
Positions of even terms in A359763, where A359763 is the Dirichlet inverse of characteristic function of the numbers with an even number of prime factors (counted with multiplicity).
[ "2", "3", "5", "7", "8", "11", "12", "13", "16", "17", "18", "19", "20", "23", "27", "28", "29", "30", "31", "32", "36", "37", "41", "42", "43", "44", "45", "47", "48", "50", "52", "53", "59", "61", "63", "64", "66", "67", "68", "70", "71", "72", "73", "75", "76", "78", "79", "80", "81", "83", "89", "92", "96", "97", "98", "99", "100", "101", "102", "103", "105", "107", "108", "109", "110", "112", "113", "114", "116", "117", "120", "124", "125", "127", "128", "130" ]
[ "nonn" ]
6
1
1
[ "A026424", "A065043", "A359763", "A359764", "A359765", "A359766", "A359767", "A359791" ]
null
Antti Karttunen, Jan 13 2023
2023-01-13T16:25:39
oeisdata/seq/A359/A359766.seq
00da40d424d0787ecb45ecf6e28cc1eb
A359767
Numbers k such that A065043(k) = 1 but A359764(k) = 0, where A359764 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with an even number of prime factors).
[ "16", "36", "64", "81", "96", "100", "160", "196", "216", "224", "225", "240", "256", "336", "352", "360", "384", "416", "441", "484", "486", "504", "528", "540", "544", "560", "576", "600", "608", "624", "625", "640", "676", "729", "736", "756", "792", "810", "816", "880", "896", "900", "912", "928", "936", "960", "992", "1000", "1024", "1040", "1089", "1104", "1134", "1156", "1176", "1184", "1188", "1215", "1224", "1225" ]
[ "nonn" ]
8
1
1
[ "A013929", "A026424", "A028260", "A065043", "A359763", "A359764", "A359765", "A359766", "A359767", "A359784" ]
null
Antti Karttunen, Jan 13 2023
2023-01-13T16:25:43
oeisdata/seq/A359/A359767.seq
e41c9acf780eedd9433610541e925d7b
A359768
a(n) = 1 if the parity of n and that of sopfr(n) differ, otherwise 0. Here sopfr is the sum of prime factors (with repetition).
[ "1", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "0", "0", "0", "1", "1", "1", "0", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "1" ]
[ "nonn" ]
13
1
null
[ "A000035", "A001414", "A036347", "A075254", "A075255", "A359768" ]
null
Antti Karttunen, Jan 15 2023
2023-11-22T10:48:12
oeisdata/seq/A359/A359768.seq
c4a1ec459a7d0036f9e8965c14dfcbe9
A359769
a(n) = A353557(n) - A353556(n).
[ "1", "-1", "0", "0", "0", "0", "0", "-1", "1", "0", "0", "-1", "0", "0", "1", "0", "0", "-1", "0", "-1", "1", "0", "0", "0", "1", "0", "0", "-1", "0", "-1", "0", "-1", "1", "0", "1", "0", "0", "0", "1", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "1", "-1", "1", "-1", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "0", "-1", "1", "-1", "0", "-1", "0", "0", "0", "-1", "1", "-1", "0", "-1", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "-1", "1", "0", "1", "0", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "-1", "1", "-1" ]
[ "sign" ]
10
1
null
[ "A001222", "A003961", "A065043", "A353556", "A353557", "A359769", "A359770", "A359814" ]
null
Antti Karttunen, Jan 15 2023
2023-11-22T10:47:38
oeisdata/seq/A359/A359769.seq
da2a816ae65d1ddde4b41fed5d5b7e24
A359770
a(n) = 1 if n and bigomega(n) are of different parity, otherwise 0. Here bigomega (A001222) gives the number of prime factors of n with multiplicity.
[ "1", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "1", "1", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "1", "1", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "1" ]
[ "nonn" ]
12
1
null
[ "A000035", "A001222", "A003961", "A065043", "A069345", "A353556", "A353557", "A359769", "A359770", "A359771", "A359772", "A359815" ]
null
Antti Karttunen, Jan 15 2023
2023-01-16T15:44:35
oeisdata/seq/A359/A359770.seq
6150cb2870ea143ef8b819e689bf6e59
A359771
Union of even numbers with an odd number of prime factors and odd numbers with an even number of prime factors, when the number of prime factors is counted with multiplicity.
[ "1", "2", "8", "9", "12", "15", "18", "20", "21", "25", "28", "30", "32", "33", "35", "39", "42", "44", "48", "49", "50", "51", "52", "55", "57", "65", "66", "68", "69", "70", "72", "76", "77", "78", "80", "81", "85", "87", "91", "92", "93", "95", "98", "102", "108", "110", "111", "112", "114", "115", "116", "119", "120", "121", "123", "124", "128", "129", "130", "133", "135", "138", "141", "143", "145", "148", "154", "155", "159", "161" ]
[ "nonn" ]
5
1
2
[ "A001222", "A046337", "A046470", "A069345", "A359770", "A359771", "A359772" ]
null
Antti Karttunen, Jan 15 2023
2023-01-15T15:09:46
oeisdata/seq/A359/A359771.seq
90473d3e7b3ade2823aaf3eec95b89e5
A359772
Union of even numbers with an even number of prime factors and odd numbers with an odd number of prime factors, when the number of prime factors is counted with multiplicity.
[ "3", "4", "5", "6", "7", "10", "11", "13", "14", "16", "17", "19", "22", "23", "24", "26", "27", "29", "31", "34", "36", "37", "38", "40", "41", "43", "45", "46", "47", "53", "54", "56", "58", "59", "60", "61", "62", "63", "64", "67", "71", "73", "74", "75", "79", "82", "83", "84", "86", "88", "89", "90", "94", "96", "97", "99", "100", "101", "103", "104", "105", "106", "107", "109", "113", "117", "118", "122", "125", "126", "127", "131", "132" ]
[ "nonn" ]
6
1
1
[ "A001222", "A063745", "A067019", "A069345", "A359770", "A359771", "A359772" ]
null
Antti Karttunen, Jan 15 2023
2023-01-15T15:09:52
oeisdata/seq/A359/A359772.seq
fd802d69b48d72f703fe62bfb5a8ccd9
A359773
Dirichlet inverse of A356163, where A356163 is the characteristic function of the numbers with an even sum of prime factors (counted with multiplicity).
[ "1", "-1", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "0", "1", "0", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "1", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "-1", "1", "-1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "-1", "1", "0", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "0", "-1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "sign" ]
21
1
225
[ "A001414", "A003961", "A036347", "A036348", "A036349", "A067019", "A335657", "A356163", "A359155", "A359763", "A359773", "A359774", "A359775", "A359776", "A359777", "A359780" ]
null
Antti Karttunen, Jan 13 2023
2023-01-15T19:50:34
oeisdata/seq/A359/A359773.seq
95bc89f7cfb6f610b295d566337746eb
A359774
Parity of A359773, where A359773 is the Dirichlet inverse of A356163.
[ "1", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "1" ]
[ "nonn" ]
14
1
null
[ "A001414", "A003961", "A356163", "A359764", "A359773", "A359774", "A359775", "A359776", "A359777", "A359787", "A359789" ]
null
Antti Karttunen, Jan 13 2023
2023-01-16T21:55:26
oeisdata/seq/A359/A359774.seq
31e89ddae1eb20ade48eead56c45d39d
A359775
Positions of odd terms in A359773, where A359773 is the Dirichlet inverse of A356163.
[ "1", "2", "9", "15", "18", "21", "25", "30", "33", "35", "39", "42", "49", "50", "51", "55", "57", "65", "66", "69", "70", "77", "78", "85", "87", "91", "93", "95", "98", "102", "110", "111", "114", "115", "119", "121", "123", "129", "130", "133", "135", "138", "141", "143", "145", "154", "155", "159", "161", "169", "170", "174", "177", "182", "183", "185", "186", "187", "189", "190", "201", "203", "205", "209", "213", "215", "217" ]
[ "nonn" ]
7
1
2
[ "A001414", "A036349", "A356163", "A359765", "A359773", "A359774", "A359775", "A359776", "A359777", "A359789" ]
null
Antti Karttunen, Jan 15 2023
2023-01-15T15:10:21
oeisdata/seq/A359/A359775.seq
2a037c20e151e9f2f766878b24f925b0
A359776
Positions of even terms in A359773, where A359773 is the Dirichlet inverse of A356163.
[ "3", "4", "5", "6", "7", "8", "10", "11", "12", "13", "14", "16", "17", "19", "20", "22", "23", "24", "26", "27", "28", "29", "31", "32", "34", "36", "37", "38", "40", "41", "43", "44", "45", "46", "47", "48", "52", "53", "54", "56", "58", "59", "60", "61", "62", "63", "64", "67", "68", "71", "72", "73", "74", "75", "76", "79", "80", "81", "82", "83", "84", "86", "88", "89", "90", "92", "94", "96", "97", "99", "100", "101", "103", "104", "105", "106" ]
[ "nonn" ]
7
1
1
[ "A001414", "A335657", "A356163", "A359766", "A359773", "A359774", "A359775", "A359776", "A359777", "A359789" ]
null
Antti Karttunen, Jan 15 2023
2023-01-15T15:10:26
oeisdata/seq/A359/A359776.seq
64c83bd7a6028772477d3e7c6753ee0e
A359777
Numbers k such that A356163(k) = 1 but A359774(k) = 0, where A359774 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with an even sum of prime factors, with repetition).
[ "4", "8", "16", "32", "36", "60", "64", "72", "81", "84", "100", "120", "128", "132", "140", "144", "156", "162", "168", "196", "200", "204", "220", "225", "228", "240", "256", "260", "264", "276", "280", "288", "308", "312", "324", "336", "340", "348", "364", "372", "380", "392", "400", "408", "440", "441", "444", "450", "456", "460", "476", "480", "484", "492", "512", "516", "520", "528", "532", "540", "552", "560", "564" ]
[ "nonn" ]
5
1
1
[ "A001414", "A036349", "A335657", "A356163", "A359767", "A359773", "A359774", "A359775", "A359776", "A359777", "A359784" ]
null
Antti Karttunen, Jan 15 2023
2023-01-15T15:10:30
oeisdata/seq/A359/A359777.seq
25811ee58f582946003914356a47324a
A359778
Number of factorizations of n into factors not divisible by p^p for any prime p (terms of A048103).
[ "1", "1", "1", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "2", "2", "1", "1", "4", "1", "2", "2", "2", "1", "2", "2", "2", "2", "2", "1", "5", "1", "1", "2", "2", "2", "5", "1", "2", "2", "2", "1", "5", "1", "2", "4", "2", "1", "2", "2", "4", "2", "2", "1", "5", "2", "2", "2", "2", "1", "6", "1", "2", "4", "1", "2", "5", "1", "2", "2", "5", "1", "5", "1", "2", "4", "2", "2", "5", "1", "2", "3", "2", "1", "6", "2", "2", "2", "2", "1", "11", "2", "2", "2", "2", "2", "2", "1", "4", "4", "5", "1", "5", "1", "2", "5", "2", "1", "7" ]
[ "nonn" ]
13
1
6
[ "A001055", "A048103", "A276086", "A317836", "A358236", "A359550", "A359778", "A359779" ]
null
Antti Karttunen, Jan 16 2023
2023-01-17T10:01:03
oeisdata/seq/A359/A359778.seq
cbc955eb571b85880cd6744682f12cd8
A359779
Dirichlet inverse of A359778, where A359778 is the number of factorizations of n into factors not divisible by p^p for any prime p (terms of A048103).
[ "1", "-1", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "-1", "1", "-1", "0", "0", "0", "-1", "1", "-1", "1", "0", "0", "-1", "0", "-1", "0", "1", "1", "-1", "1", "-1", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "1", "-1", "1", "1", "0", "-1", "0", "-1", "1", "0", "1", "-1", "1", "0", "0", "0", "0", "-1", "0", "-1", "0", "1", "0", "0", "1", "-1", "1", "0", "1", "-1", "0", "-1", "0", "1", "1", "0", "1", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "1", "0", "1", "0", "0", "0", "0", "-1", "1", "1", "0", "-1", "1", "-1", "0", "1" ]
[ "sign" ]
8
1
420
[ "A048103", "A359550", "A359778", "A359779" ]
null
Antti Karttunen, Jan 16 2023
2023-01-17T10:01:09
oeisdata/seq/A359/A359779.seq
3fd7f212d675e446c64839a076db5536
A359780
Dirichlet inverse of A358680, where A358680 is the characteristic function of the numbers with even arithmetic derivative (A003415).
[ "1", "0", "0", "-1", "0", "0", "0", "-1", "-1", "0", "0", "-1", "0", "0", "-1", "0", "0", "0", "0", "-1", "-1", "0", "0", "-1", "-1", "0", "0", "-1", "0", "0", "0", "1", "-1", "0", "-1", "1", "0", "0", "-1", "-1", "0", "0", "0", "-1", "0", "0", "0", "1", "-1", "0", "-1", "-1", "0", "0", "-1", "-1", "-1", "0", "0", "1", "0", "0", "0", "1", "-1", "0", "0", "-1", "-1", "0", "0", "1", "0", "0", "0", "-1", "-1", "0", "0", "1", "0", "0", "0", "1", "-1", "0", "-1", "-1", "0", "0", "-1", "-1", "-1", "0", "-1", "3", "0", "0", "0", "1", "0", "0", "0", "-1", "0" ]
[ "sign" ]
25
1
96
[ "A003415", "A003961", "A016825", "A067019", "A235992", "A353348", "A358680", "A359763", "A359780", "A359781", "A359782", "A359783", "A359784", "A359793", "A359823" ]
null
Antti Karttunen, Jan 13 2023
2023-01-17T16:31:12
oeisdata/seq/A359/A359780.seq
d6cd61bf60a4868b0b00cf161c5300a1
A359781
Parity of A359780, where A359780 is the Dirichlet inverse of the characteristic function of the numbers with even arithmetic derivative (A003415).
[ "1", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "1", "0", "0", "0", "0" ]
[ "nonn" ]
16
1
null
[ "A003961", "A056913", "A358680", "A359764", "A359774", "A359780", "A359781", "A359782", "A359783", "A359784", "A359790" ]
null
Antti Karttunen, Jan 13 2023
2025-03-25T02:31:22
oeisdata/seq/A359/A359781.seq
385a71d75a260648d2c50656aa7fcc35
A359782
Positions of even terms in A359780.
[ "2", "3", "5", "6", "7", "10", "11", "13", "14", "16", "17", "18", "19", "22", "23", "26", "27", "29", "30", "31", "34", "37", "38", "41", "42", "43", "45", "46", "47", "50", "53", "54", "58", "59", "61", "62", "63", "66", "67", "70", "71", "73", "74", "75", "78", "79", "81", "82", "83", "86", "89", "90", "94", "97", "98", "99", "101", "102", "103", "105", "106", "107", "109", "110", "113", "114", "117", "118", "122", "125", "126", "127", "128", "130", "131" ]
[ "nonn" ]
8
1
1
[ "A235991", "A358680", "A359780", "A359781", "A359782", "A359783", "A359784", "A359790" ]
null
Antti Karttunen, Jan 13 2023
2023-01-14T12:41:07
oeisdata/seq/A359/A359782.seq
9fd91f75b8aaea2e16e91579606fff55
A359783
Positions of odd terms in A359780.
[ "1", "4", "8", "9", "12", "15", "20", "21", "24", "25", "28", "32", "33", "35", "36", "39", "40", "44", "48", "49", "51", "52", "55", "56", "57", "60", "64", "65", "68", "69", "72", "76", "77", "80", "84", "85", "87", "88", "91", "92", "93", "95", "96", "100", "104", "108", "111", "112", "115", "116", "119", "120", "121", "123", "124", "129", "132", "133", "135", "136", "140", "141", "143", "144", "145", "148", "152", "155", "156", "159", "160", "161" ]
[ "nonn" ]
9
1
2
[ "A003415", "A056913", "A235992", "A358680", "A359765", "A359780", "A359781", "A359782", "A359783", "A359784", "A359790", "A359825" ]
null
Antti Karttunen, Jan 13 2023
2023-01-14T12:40:10
oeisdata/seq/A359/A359783.seq
363b68dda75c9826b5a28a815f22fcbf
A359784
Numbers k such that A358680(k) = 1 but A359781(k) = 0, where A359781 is the parity of Dirichlet inverse of the former (which is the characteristic function of the numbers with even arithmetic derivative).
[ "16", "81", "128", "192", "225", "240", "320", "324", "336", "384", "441", "448", "528", "560", "624", "625", "640", "648", "704", "729", "816", "832", "880", "896", "900", "912", "972", "1024", "1040", "1088", "1089", "1104", "1215", "1216", "1225", "1232", "1360", "1392", "1408", "1456", "1472", "1488", "1520", "1521", "1620", "1664", "1701", "1764", "1776", "1800", "1840", "1856", "1904", "1920", "1944", "1968", "1984" ]
[ "nonn" ]
7
1
1
[ "A003415", "A013929", "A235991", "A235992", "A358680", "A359767", "A359780", "A359781", "A359782", "A359783", "A359784" ]
null
Antti Karttunen, Jan 13 2023
2023-01-14T12:40:03
oeisdata/seq/A359/A359784.seq
3519e7cd5de11732f8ed3a251026e883
A359785
Dirichlet inverse of A320655, where A320655(n) is the number of factorizations of n into semiprimes.
[ "1", "0", "0", "-1", "0", "-1", "0", "0", "-1", "-1", "0", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "-1", "-1", "0", "1", "-1", "-1", "0", "0", "0", "0", "0", "0", "-1", "-1", "-1", "1", "0", "-1", "-1", "1", "0", "0", "0", "0", "0", "-1", "0", "0", "-1", "0", "-1", "0", "0", "1", "-1", "1", "-1", "-1", "0", "2", "0", "-1", "0", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "-1", "0", "0", "-1", "0", "0", "0", "0", "-1", "0", "2", "-1", "-1", "-1", "1", "0", "2", "-1", "0", "-1", "-1", "-1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0" ]
[ "sign" ]
9
1
60
[ "A320655", "A322353", "A359785", "A359786" ]
null
Antti Karttunen, Jan 16 2023
2023-10-05T16:25:15
oeisdata/seq/A359/A359785.seq
ba1a1aa6aa1884161af1cbf5496531ae
A359786
Dirichlet inverse of A322353, where A322353(n) is the number of factorizations of n into distinct semiprimes.
[ "1", "0", "0", "-1", "0", "-1", "0", "0", "-1", "-1", "0", "0", "0", "-1", "-1", "1", "0", "0", "0", "0", "-1", "-1", "0", "1", "-1", "-1", "0", "0", "0", "0", "0", "0", "-1", "-1", "-1", "2", "0", "-1", "-1", "1", "0", "0", "0", "0", "0", "-1", "0", "0", "-1", "0", "-1", "0", "0", "1", "-1", "1", "-1", "-1", "0", "2", "0", "-1", "0", "-1", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "-1", "0", "0", "-1", "0", "0", "0", "1", "-1", "0", "2", "-1", "-1", "-1", "1", "0", "2", "-1", "0", "-1", "-1", "-1", "-1", "0", "0", "0", "2", "0", "0", "0", "1", "0" ]
[ "sign" ]
8
1
36
[ "A320655", "A322353", "A359785", "A359786" ]
null
Antti Karttunen, Jan 16 2023
2023-10-05T16:25:21
oeisdata/seq/A359/A359786.seq
3f90591db1adddd7ce14571e6e1594af
A359787
Parity of Dirichlet inverse of A075255, where A075255(n) = n - sopfr(n), where sopfr is the sum of prime factors (with repetition).
[ "1", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "0", "0", "0", "1", "1", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "1" ]
[ "nonn" ]
11
1
null
[ "A001414", "A003961", "A075255", "A359764", "A359768", "A359774", "A359787", "A359788", "A359816" ]
null
Antti Karttunen, Jan 16 2023
2023-01-17T10:01:14
oeisdata/seq/A359/A359787.seq
0871f5e4cfe8bf833356f0c8303b7d12
A359788
Dirichlet inverse of A075255, where A075255(n) = n - sopfr(n), where sopfr is the sum of prime factors (with repetition).
[ "1", "0", "0", "0", "0", "-1", "0", "-2", "-3", "-3", "0", "-5", "0", "-5", "-7", "-8", "0", "-10", "0", "-11", "-11", "-9", "0", "-15", "-15", "-11", "-18", "-17", "0", "-20", "0", "-22", "-19", "-15", "-23", "-25", "0", "-17", "-23", "-29", "0", "-30", "0", "-29", "-34", "-21", "0", "-33", "-35", "-38", "-31", "-35", "0", "-37", "-39", "-43", "-35", "-27", "0", "-42", "0", "-29", "-50", "-48", "-47", "-50", "0", "-47", "-43", "-56", "0", "-38", "0", "-35" ]
[ "sign" ]
8
1
8
[ "A001414", "A075255", "A359787", "A359788", "A359789" ]
null
Antti Karttunen, Jan 15 2023
2023-01-16T21:55:43
oeisdata/seq/A359/A359788.seq
b4efd06d129f573f470fe962898ba1df
A359789
Dirichlet inverse of A036288, where A036288(n) = 1 + sopfr(n), where sopfr is the sum of prime divisors with repetition, A001414.
[ "1", "-3", "-4", "4", "-6", "18", "-8", "-4", "9", "28", "-12", "-40", "-14", "38", "39", "4", "-18", "-63", "-20", "-64", "53", "58", "-24", "64", "25", "68", "-18", "-88", "-30", "-253", "-32", "-4", "81", "88", "83", "216", "-38", "98", "95", "104", "-42", "-347", "-44", "-136", "-144", "118", "-48", "-88", "49", "-175", "123", "-160", "-54", "180", "127", "144", "137", "148", "-60", "820", "-62", "158", "-198", "4", "149", "-535" ]
[ "sign" ]
8
1
2
[ "A001414", "A036288", "A359773", "A359774", "A359788", "A359789", "A359790", "A359791" ]
null
Antti Karttunen, Jan 15 2023
2023-01-17T10:01:19
oeisdata/seq/A359/A359789.seq
1a86a9586e76ccf96b422d2ccd4f8f36
A359790
Dirichlet inverse of function f(n) = 1 + n', where n' stands for the arithmetic derivative of n, A003415(n).
[ "1", "-2", "-2", "-1", "-2", "2", "-2", "-1", "-3", "0", "-2", "3", "-2", "-2", "-1", "0", "-2", "6", "-2", "3", "-3", "-6", "-2", "7", "-7", "-8", "-8", "3", "-2", "12", "-2", "3", "-7", "-12", "-5", "9", "-2", "-14", "-9", "11", "-2", "18", "-2", "3", "0", "-18", "-2", "11", "-11", "6", "-13", "3", "-2", "26", "-9", "15", "-15", "-24", "-2", "17", "-2", "-26", "-4", "9", "-11", "30", "-2", "3", "-19", "16", "-2", "9", "-2", "-32", "0", "3", "-11", "36", "-2", "23", "-16", "-36" ]
[ "sign" ]
12
1
2
[ "A003415", "A003961", "A346241", "A347082", "A347084", "A359603", "A359780", "A359781", "A359782", "A359783", "A359789", "A359790", "A359791" ]
null
Antti Karttunen, Jan 13 2023
2023-01-17T10:01:24
oeisdata/seq/A359/A359790.seq
22e4e352a373b97e8c36daaf13ddcf35
A359791
Dirichlet inverse of function f(n) = 1 + A349905(n), where A349905(n) is the arithmetic derivative of prime shifted n.
[ "1", "-2", "-2", "-3", "-2", "-1", "-2", "-8", "-7", "-3", "-2", "0", "-2", "-7", "-5", "-16", "-2", "0", "-2", "-4", "-9", "-9", "-2", "23", "-11", "-13", "-40", "-12", "-2", "12", "-2", "-16", "-11", "-15", "-11", "42", "-2", "-19", "-15", "21", "-2", "12", "-2", "-16", "-24", "-25", "-2", "128", "-19", "-12", "-17", "-24", "-2", "67", "-13", "17", "-21", "-27", "-2", "105", "-2", "-33", "-48", "48", "-17", "12", "-2", "-28", "-27", "0", "-2", "224" ]
[ "sign" ]
7
1
2
[ "A003415", "A003961", "A349905", "A359169", "A359764", "A359765", "A359766", "A359790", "A359791" ]
null
Antti Karttunen, Jan 13 2023
2023-01-17T10:01:28
oeisdata/seq/A359/A359791.seq
1efe84436d08b81a1439ad0af420f53a
A359792
a(n) = (-1)^A003415(n), where A003415 is the arithmetic derivative of n.
[ "1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "-1", "-1", "1", "-1", "-1", "1", "1", "-1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "-1", "1", "1", "-1", "-1", "1", "1", "1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "-1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "-1", "1", "1", "-1", "1", "1", "-1", "-1", "1", "1", "1", "-1", "1", "1", "-1", "-1", "-1", "1", "-1", "-1", "-1", "1", "-1" ]
[ "sign" ]
7
1
null
[ "A003415", "A165560", "A358680", "A359792", "A359793" ]
null
Antti Karttunen, Jan 14 2023
2023-01-14T18:36:51
oeisdata/seq/A359/A359792.seq
d0ec5c54677cd69743ebb585c69167f2
A359793
Dirichlet inverse of (-1)^A003415(n), where A003415 is the arithmetic derivative of n.
[ "1", "1", "1", "0", "1", "3", "1", "-2", "0", "3", "1", "2", "1", "3", "1", "-4", "1", "4", "1", "2", "1", "3", "1", "-6", "0", "3", "0", "2", "1", "9", "1", "-4", "1", "3", "1", "8", "1", "3", "1", "-6", "1", "9", "1", "2", "0", "3", "1", "-20", "0", "4", "1", "2", "1", "4", "1", "-6", "1", "3", "1", "16", "1", "3", "0", "0", "1", "9", "1", "2", "1", "9", "1", "-4", "1", "3", "0", "2", "1", "9", "1", "-20", "0", "3", "1", "16", "1", "3", "1", "-6", "1", "12", "1", "2", "1", "3", "1", "-28", "1", "4", "0" ]
[ "sign" ]
10
1
6
[ "A003415", "A005117", "A008966", "A013929", "A359780", "A359792", "A359793", "A359823" ]
null
Antti Karttunen, Jan 14 2023
2023-01-14T18:37:15
oeisdata/seq/A359/A359793.seq
4e1e1e446f3316c2da96b6f6b1629ee7
A359794
Union of odd numbers and numbers with an odd 2-adic valuation.
[ "1", "2", "3", "5", "6", "7", "8", "9", "10", "11", "13", "14", "15", "17", "18", "19", "21", "22", "23", "24", "25", "26", "27", "29", "30", "31", "32", "33", "34", "35", "37", "38", "39", "40", "41", "42", "43", "45", "46", "47", "49", "50", "51", "53", "54", "55", "56", "57", "58", "59", "61", "62", "63", "65", "66", "67", "69", "70", "71", "72", "73", "74", "75", "77", "78", "79", "81", "82", "83", "85", "86", "87", "88", "89", "90", "91", "93", "94" ]
[ "nonn" ]
13
1
2
[ "A005408", "A036554", "A048675", "A108269", "A359794", "A359832" ]
null
Antti Karttunen, Jan 25 2023
2025-01-29T14:33:28
oeisdata/seq/A359/A359794.seq
6fe792ae2c41588f5b7bc1d7fa167a05
A359795
Dirichlet inverse of function f(n) = 1 + A048675(n), where A048675(n) is fully additive with a(p) = 2^(1-PrimePi(p)).
[ "1", "-2", "-3", "1", "-5", "8", "-9", "0", "4", "14", "-17", "-7", "-33", "26", "23", "0", "-65", "-16", "-129", "-13", "43", "50", "-257", "2", "16", "98", "-4", "-25", "-513", "-84", "-1025", "0", "83", "194", "77", "24", "-2049", "386", "163", "4", "-4097", "-160", "-8193", "-49", "-52", "770", "-16385", "0", "64", "-64", "323", "-97", "-32769", "24", "149", "8", "643", "1538", "-65537", "115", "-131073", "3074", "-100" ]
[ "sign" ]
16
1
2
[ "A000720", "A048675", "A091428", "A353348", "A359592", "A359603", "A359789", "A359790", "A359791", "A359795" ]
null
Antti Karttunen, Jan 26 2023
2023-01-26T16:13:21
oeisdata/seq/A359/A359795.seq
c8ab20f7a0468232a5bde15e07664882
A359796
a(n) = Sum_{d|n} (2*d)^(d-1).
[ "1", "5", "37", "517", "10001", "248873", "7529537", "268435973", "11019960613", "512000010005", "26559922791425", "1521681143418409", "95428956661682177", "6502111422505477189", "478296900000000010037", "37778931862957430145541", "3189059870763703892770817" ]
[ "nonn", "easy" ]
12
1
2
[ "A262843", "A359731", "A359796" ]
null
Seiichi Manyama, Jan 13 2023
2023-08-14T02:00:29
oeisdata/seq/A359/A359796.seq
a15ba72f83e661ea362771321d1b769f
A359797
Cogrowth sequence of the lamplighter group Z_2 wr Z where wr denotes the wreath product.
[ "1", "3", "15", "87", "547", "3623", "24885", "175591", "1265187", "9271167", "68894785", "518053231", "3935274277", "30158804835", "232930956175", "1811476156847", "14174669041427", "111532445963367", "882004732285473", "7006931317108119", "55899039962599777", "447666261592033123" ]
[ "nonn", "walk" ]
19
0
2
[ "A288348", "A359797", "A359798" ]
null
Andrew Elvey Price, Jan 13 2023
2023-07-30T19:10:13
oeisdata/seq/A359/A359797.seq
76dbe050fa2f505955dece052ea52c52
A359798
Cogrowth sequence of the group Z wr Z where wr denotes the wreath product.
[ "1", "4", "28", "232", "2108", "20384", "206392", "2165720", "23385340", "258532216", "2915343808", "33437862352", "389230520888", "4590271681064", "54767161155000", "660307913374352", "8036973478493436", "98672644594401736", "1221090110502080440", "15222093531642444504" ]
[ "nonn" ]
26
0
2
[ "A294782", "A359705", "A359797", "A359798" ]
null
Andrew Elvey Price, Jan 13 2023
2023-07-30T18:22:36
oeisdata/seq/A359/A359798.seq
c0da7cd3e0aef211902505b6e1bf24c1
A359799
a(1) = 1, a(2) = 3; for n > 2, a(n) is the smallest positive number which has not appeared that shares a factor with |a(n-1) - a(n-2)| while the difference |a(n) - a(n-1)| is distinct from all previous differences |a(i) - a(i-1)|, i=2..n-1.
[ "1", "3", "6", "12", "2", "10", "14", "26", "4", "11", "28", "17", "22", "35", "65", "5", "20", "36", "8", "32", "9", "23", "42", "76", "18", "38", "56", "15", "41", "16", "25", "54", "87", "21", "48", "27", "63", "24", "66", "7", "59", "13", "44", "93", "49", "84", "30", "62", "100", "19", "69", "106", "37", "90", "212", "34", "74", "122", "33", "89", "46", "129", "249", "39", "86", "141", "40", "101", "183", "50", "95", "159", "52" ]
[ "nonn" ]
8
1
2
[ "A337136", "A352763", "A353989", "A354087", "A354687", "A354727", "A354753", "A354755", "A359799", "A361314" ]
null
Scott R. Shannon, Mar 07 2023
2023-03-09T06:18:02
oeisdata/seq/A359/A359799.seq
758ed980f6432ae5863209595bd5b024
A359800
a(n) is the least m such that the concatenation of n^2 and m is a square.
[ "6", "9", "61", "9", "6", "1", "284", "516", "225", "489", "104", "4", "744", "249", "625", "3201", "444", "9", "201", "689", "4201", "416", "984", "4801", "681", "5201", "316", "996", "5801", "601", "6201", "144", "936", "6801", "449", "7201", "7401", "804", "7801", "225", "8201", "8401", "6", "8801", "9001", "9201", "9401", "324", "9801", "19344", "769", "38025" ]
[ "nonn", "look", "base" ]
64
1
1
[ "A000290", "A071176", "A075836", "A084070", "A221874", "A246560", "A359800" ]
null
Mohammed Yaseen, Jan 13 2023
2023-02-16T15:15:29
oeisdata/seq/A359/A359800.seq
ed9f4838cb59fcae6b8c4ab35bc23be1