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348
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score
int64
1
2.31k
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int64
-14,827
666,262,453B
offset_b
int64
0
635M
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cross_references
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128
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A361601
Decimal expansion of the maximum possible disorientation angle between two identical cubes (in radians).
[ "1", "0", "9", "6", "0", "5", "6", "8", "1", "5", "2", "4", "0", "6", "2", "5", "4", "8", "9", "0", "6", "1", "7", "2", "6", "5", "6", "5", "6", "4", "1", "2", "5", "7", "3", "5", "6", "9", "5", "9", "4", "2", "4", "7", "2", "7", "3", "1", "8", "4", "0", "8", "6", "3", "3", "9", "9", "1", "0", "9", "6", "8", "7", "7", "7", "2", "0", "6", "7", "8", "8", "7", "1", "0", "9", "2", "9", "7", "0", "9", "1", "0", "7", "7", "9", "8", "7", "0", "6", "3", "1", "4", "8", "8", "8", "2", "5", "7", "5", "7", "5", "7", "6", "9", "1" ]
[ "nonn", "cons" ]
9
1
3
[ "A003881", "A201488", "A361601", "A361602", "A361603", "A361604" ]
null
Amiram Eldar, Mar 17 2023
2025-02-10T08:44:47
oeisdata/seq/A361/A361601.seq
72da2c2c578abb028f24736be4977612
A361602
Decimal expansion of the mean of the distribution of disorientation angles between two identical cubes (in radians).
[ "7", "1", "0", "9", "7", "4", "6", "0", "7", "6", "8", "6", "0", "5", "9", "1", "1", "9", "1", "6", "4", "3", "8", "9", "4", "4", "0", "4", "1", "5", "3", "7", "0", "1", "4", "9", "3", "3", "9", "2", "8", "6", "2", "1", "0", "3", "9", "4", "7", "6", "0", "5", "6", "3", "0", "7", "4", "1", "2", "3", "7", "4", "8", "0", "4", "2", "3", "8", "0", "0", "7", "2", "4", "4", "1", "5", "8", "7", "6", "7", "8", "7", "9", "1", "0", "5", "1", "3", "3", "2", "0", "4", "4", "7", "2", "6", "8", "6", "0", "6", "7", "2", "7", "1", "2" ]
[ "nonn", "cons" ]
12
0
1
[ "A361601", "A361602", "A361603", "A361604" ]
null
Amiram Eldar, Mar 17 2023
2025-04-13T03:19:25
oeisdata/seq/A361/A361602.seq
7c53a05c1413854da81afe939448ebe6
A361603
Decimal expansion of the standard deviation of the distribution of disorientation angles between two identical cubes (in radians).
[ "1", "9", "7", "4", "8", "3", "0", "2", "6", "7", "7", "9", "4", "9", "4", "1", "6", "4", "0", "2", "6", "0", "7", "9", "9", "2", "7", "7", "5", "3", "7", "8", "4", "2", "5", "4", "9", "8", "5", "3", "8", "6", "4", "7", "6", "3", "0", "2", "9", "8", "4", "5", "3", "7", "0", "8", "4", "9", "7", "9", "7", "4", "2", "3", "0", "3", "4", "2", "9", "1", "5", "2", "8", "1", "2", "1", "9", "1", "2", "7", "1", "8", "5", "7", "6", "0", "5", "5", "8", "0", "2", "5", "2", "6", "0", "6", "8", "1", "6", "1", "7", "7", "6", "9", "2" ]
[ "nonn", "cons" ]
12
0
2
[ "A361601", "A361602", "A361603", "A361604" ]
null
Amiram Eldar, Mar 17 2023
2025-04-13T03:19:29
oeisdata/seq/A361/A361603.seq
33cc40c56485b6fc5e164d708ca139ac
A361604
Decimal expansion of the median of the distribution of disorientation angles between two identical cubes (in radians).
[ "7", "3", "8", "9", "9", "5", "9", "8", "6", "2", "8", "7", "6", "0", "5", "1", "0", "1", "7", "9", "6", "3", "4", "1", "1", "3", "5", "6", "1", "5", "8", "3", "5", "8", "2", "4", "7", "6", "4", "8", "1", "5", "9", "1", "7", "6", "4", "7", "0", "6", "0", "2", "0", "9", "4", "3", "0", "0", "4", "9", "7", "8", "0", "3", "0", "0", "5", "8", "7", "8", "3", "6", "3", "1", "8", "7", "1", "3", "8", "6", "4", "6", "1", "7", "2", "9", "7", "4", "8", "3", "7", "4", "5", "7", "0", "9", "1", "3", "6", "8", "0", "3", "0", "0", "3" ]
[ "nonn", "cons" ]
10
0
1
[ "A361601", "A361602", "A361603", "A361604" ]
null
Amiram Eldar, Mar 17 2023
2025-03-26T08:32:08
oeisdata/seq/A361/A361604.seq
c47143238b40e9568919433d063158fe
A361605
Decimal expansion of the standard deviation of the probability distribution function of angles of random rotations in 3D space uniformly distributed with respect to Haar measure (in radians).
[ "6", "4", "5", "8", "9", "6", "5", "0", "7", "8", "5", "1", "4", "9", "9", "4", "8", "2", "3", "5", "8", "7", "4", "1", "3", "8", "4", "2", "6", "5", "5", "2", "7", "1", "6", "2", "1", "6", "7", "5", "0", "3", "2", "6", "3", "0", "6", "1", "1", "1", "1", "7", "0", "2", "7", "3", "2", "9", "1", "2", "0", "4", "9", "9", "3", "8", "5", "5", "1", "4", "6", "1", "9", "3", "6", "7", "7", "7", "5", "7", "2", "1", "7", "1", "5", "2", "5", "9", "5", "1", "1", "4", "9", "1", "6", "6", "3", "5", "0", "5", "2", "1", "0", "8", "0" ]
[ "nonn", "cons" ]
12
0
1
[ "A086118", "A336083", "A361605" ]
null
Amiram Eldar, Mar 17 2023
2023-03-17T08:08:43
oeisdata/seq/A361/A361605.seq
34a5704cd1e382b7c2365d62fd8ea2c8
A361606
Lexicographically earliest infinite sequence of distinct positive numbers such that, for n > 3, a(n) shares a factor with a(n-1) and a(n-2) but not with a(n-1) + a(n-2).
[ "1", "6", "10", "15", "12", "20", "45", "18", "40", "75", "24", "50", "105", "14", "30", "21", "28", "36", "63", "56", "48", "147", "98", "54", "189", "70", "60", "231", "22", "42", "33", "44", "72", "99", "88", "78", "143", "66", "26", "39", "84", "52", "91", "112", "104", "455", "80", "126", "35", "90", "154", "55", "100", "132", "135", "110", "96", "165", "130", "102", "85", "120", "34", "51", "108", "68", "153", "114" ]
[ "nonn" ]
25
1
2
[ "A251604", "A251622", "A336957", "A349493", "A351001", "A352774", "A352867", "A360209", "A360519", "A361102", "A361606" ]
null
Scott R. Shannon, Mar 17 2023
2023-03-18T08:09:37
oeisdata/seq/A361/A361606.seq
3c40d2841df1fe43d940d6336dc7bbb7
A361607
a(n) = n! * Sum_{k=0..n} binomial(n+(n-1)*k,n*k)/k!.
[ "1", "2", "9", "88", "1457", "35226", "1158097", "49554464", "2664907233", "175012404562", "13725980234201", "1263867766626312", "134795551989905809", "16464112185873351338", "2280346417134518709537", "355060682992984062716176" ]
[ "nonn" ]
15
0
2
[ "A293013", "A361600", "A361607" ]
null
Seiichi Manyama, Mar 17 2023
2023-03-17T09:24:25
oeisdata/seq/A361/A361607.seq
57f83027d7fd44cec88024575f970577
A361608
a(n) = 7^n*(n+1)*(81*n^4+684*n^3+1401*n^2+434*n+40)/40.
[ "1", "924", "48804", "1337014", "26622288", "437049228", "6295986235", "82489361052", "1005444707211", "11576481361732", "127278262644918", "1346951022678114", "13803666582387682", "137633164619393268", "1340161331495822661", "12782144706910135480", "119711031072135899781", "1103157160378734314700", "10019811250265958667288" ]
[ "nonn", "easy" ]
24
0
2
[ "A027471", "A361608", "A361609", "A361610" ]
null
R. J. Mathar, Mar 17 2023
2024-06-10T10:31:58
oeisdata/seq/A361/A361608.seq
95942aa562b2a60f4b05e3ecaf6f3450
A361609
a(n) = 4^n*(1 + (23/8)*n + (9/8)*n^2).
[ "1", "20", "180", "1264", "7808", "44544", "240640", "1249280", "6291456", "30932992", "149159936", "707788800", "3313500160", "15334375424", "70262980608", "319169757184", "1438814044160", "6442450944000", "28673201668096", "126924873531392", "559101662724096", "2451910929940480", "10709243254538240", "46601700831657984" ]
[ "nonn", "easy" ]
27
0
2
[ "A027471", "A361608", "A361609", "A361610" ]
null
R. J. Mathar, Mar 17 2023
2024-06-10T00:13:32
oeisdata/seq/A361/A361609.seq
a61b4a2934f0d2a276355c6cdc004f47
A361610
a(n) = 5^n*(n+1)*(4*n^2+14*n+3)/3.
[ "1", "70", "1175", "13500", "128125", "1081250", "8421875", "61875000", "434765625", "2949218750", "19443359375", "125195312500", "790283203125", "4904785156250", "29998779296875", "181152343750000", "1081695556640625", "6394958496093750", "37471771240234375", "217819213867187500", "1257038116455078125" ]
[ "nonn", "easy" ]
17
0
2
[ "A027471", "A361608", "A361609", "A361610" ]
null
R. J. Mathar, Mar 17 2023
2024-08-29T17:17:47
oeisdata/seq/A361/A361610.seq
eae204798c0187a0f16eabd528d7740e
A361611
Lexicographically least increasing sequence of semiprimes a(n) such that a(n) - a(n-1) and a(n) + a(n-1) are also semiprimes.
[ "4", "10", "25", "94", "115", "206", "221", "298", "391", "478", "511", "526", "551", "586", "655", "694", "703", "758", "779", "934", "949", "974", "989", "993", "1126", "1159", "1418", "1513", "1522", "1555", "1594", "1603", "1658", "1679", "1718", "1769", "2018", "2051", "2066", "2105", "2174", "2195", "2234", "2319", "2462", "2501", "2578", "2587", "2846", "2867", "2906", "2931", "2986", "3007" ]
[ "nonn" ]
12
1
1
[ "A001358", "A361611" ]
null
Zak Seidov and Robert Israel, Mar 17 2023
2023-04-04T19:48:32
oeisdata/seq/A361/A361611.seq
687de5982823cddedf56e5905bb95f5d
A361612
Decimal expansion of sqrt(10) truncated to n places (after the decimal point).
[ "3", "31", "316", "3162", "31622", "316227", "3162277", "31622776", "316227766", "3162277660", "31622776601", "316227766016", "3162277660168", "31622776601683", "316227766016837", "3162277660168379", "31622776601683793", "316227766016837933", "3162277660168379331", "31622776601683793319" ]
[ "nonn" ]
33
0
1
[ "A010467", "A011547", "A017934", "A361612" ]
null
Amit Katz, Mar 17 2023
2024-07-25T10:44:24
oeisdata/seq/A361/A361612.seq
9b8b6c82ec8999513ea71fb05cbd0f18
A361613
The number of magic quad squares that can be formed using cards from Quads-2^n deck.
[ "3225600", "27398246400", "58912149381120", "35354354296504320", "13112764372566835200", "3994995853001760768000", "1112834567045660389539840", "296989774972633598731223040", "77616116494664898347650252800", "20075253208336550377420672204800", "5165728566421154658646365736796160" ]
[ "nonn", "easy" ]
22
4
1
[ "A361495", "A361613", "A362874", "A362963", "A362964" ]
null
Tanya Khovanova and MIT PRIMES STEP senior group, May 11 2023
2023-08-09T18:19:16
oeisdata/seq/A361/A361613.seq
edf9745cf19bfe26b98f31b3352f1d36
A361614
Set a(1)=0 and a(2)=1. For n > 1, if a(n) has already appeared in the sequence, then a(n+1) = number of steps since its first appearance. If a(n) has not appeared before, search instead for a(n)-1, then a(n)-2, etc., until you find a number that has appeared before.
[ "0", "1", "1", "1", "2", "3", "1", "5", "2", "4", "4", "1", "10", "5", "6", "7", "1", "15", "5", "11", "7", "5", "14", "3", "18", "7", "10", "14", "5", "21", "5", "23", "2", "28", "2", "30", "2", "32", "2", "34", "2", "36", "2", "38", "2", "40", "2", "42", "2", "44", "2", "46", "2", "48", "2", "50", "2", "52", "2", "54", "2", "56", "2", "58", "2", "60", "2", "62", "2", "64", "2", "66", "2", "68", "2", "70", "2" ]
[ "nonn", "easy" ]
11
1
5
[ "A181391", "A328294", "A361614" ]
null
Robin Powell, Mar 17 2023
2023-04-09T02:29:13
oeisdata/seq/A361/A361614.seq
73ea16262329009b70666228cf16a61b
A361615
a(n) is the smallest 5-rough number with exactly n divisors.
[ "1", "5", "25", "35", "625", "175", "15625", "385", "1225", "4375", "9765625", "1925", "244140625", "109375", "30625", "5005", "152587890625", "13475", "3814697265625", "48125", "765625", "68359375", "2384185791015625", "25025", "1500625", "1708984375", "148225", "1203125", "37252902984619140625", "336875", "931322574615478515625" ]
[ "nonn" ]
9
1
2
[ "A000005", "A005179", "A007310", "A038547", "A361615" ]
null
Jon E. Schoenfield, Mar 18 2023
2023-03-18T03:24:07
oeisdata/seq/A361/A361615.seq
46a740bfe0bac8c7906ea03f352717e8
A361616
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..n} binomial(n+(k-1)*(j+1),n-j)/j!.
[ "1", "1", "1", "1", "2", "1", "1", "3", "7", "1", "1", "4", "15", "34", "1", "1", "5", "25", "103", "209", "1", "1", "6", "37", "214", "885", "1546", "1", "1", "7", "51", "373", "2293", "9051", "13327", "1", "1", "8", "67", "586", "4721", "29176", "106843", "130922", "1", "1", "9", "85", "859", "8481", "70981", "427189", "1425495", "1441729", "1" ]
[ "nonn", "tabl" ]
23
0
5
[ "A000012", "A002720", "A293985", "A343884", "A351767", "A361600", "A361616", "A361617" ]
null
Seiichi Manyama, Mar 18 2023
2023-03-26T11:09:39
oeisdata/seq/A361/A361616.seq
8163f43ecab71be68eb9f7f42ddcdb9f
A361617
a(n) = n! * Sum_{k=0..n} binomial(n+(n-1)*(k+1),n-k)/k!.
[ "1", "2", "15", "214", "4721", "146046", "5958367", "307382090", "19459587009", "1478414285146", "132440451881231", "13787717744245182", "1647673524863409265", "223671725058601427414", "34184743554559413628191", "5837132027535188545269106", "1106136052471647285563082497" ]
[ "nonn" ]
15
0
2
[ "A361607", "A361616", "A361617" ]
null
Seiichi Manyama, Mar 18 2023
2023-03-18T18:37:50
oeisdata/seq/A361/A361617.seq
d48186b6af0495b9f60e60adfa41b49b
A361618
Decimal expansion of the mean of the distribution of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians).
[ "4", "0", "4", "2", "8", "3", "3", "4", "5", "0", "4", "4", "8", "9", "3", "5", "8", "5" ]
[ "nonn", "cons", "more" ]
8
0
1
[ "A228496", "A361601", "A361618", "A361619", "A361620", "A361621" ]
null
Amiram Eldar, Mar 18 2023
2023-03-19T08:29:36
oeisdata/seq/A361/A361618.seq
f0ee742ccdfa097a473b9a5016f10e05
A361619
Decimal expansion of the standard deviation of the distribution of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians).
[ "1", "7", "9", "9", "7", "3", "0", "7", "2", "2", "8", "8", "5", "8", "0", "1", "2", "3" ]
[ "nonn", "cons", "more" ]
5
0
2
[ "A228496", "A361601", "A361618", "A361619", "A361620", "A361621" ]
null
Amiram Eldar, Mar 18 2023
2023-03-19T08:29:32
oeisdata/seq/A361/A361619.seq
6e38286837b8cfbfaa5b50ae077b38e4
A361620
Decimal expansion of the median of the distribution of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians).
[ "4", "0", "4", "6", "2", "6", "8", "0", "0", "8", "3", "8", "5", "0", "1", "3", "8", "4", "7", "5", "1", "4", "4", "5", "0", "0", "3", "5", "7", "4", "1", "4", "1", "8", "3", "6", "4", "7", "2", "6", "7", "2", "3", "3", "6", "3", "2", "8", "7", "8", "7", "1", "8", "8", "0", "0", "2", "1", "0", "5", "9", "0", "6", "4", "9", "0", "1", "2", "9", "7", "2", "4", "8", "6", "7", "3", "5", "2", "3", "2", "0", "8", "3", "1", "7", "2", "2", "6", "8", "7", "8", "9", "1", "7", "1", "8", "2", "7", "8", "7", "9", "1", "0", "9", "7" ]
[ "nonn", "cons" ]
6
0
1
[ "A228496", "A361601", "A361618", "A361619", "A361620", "A361621" ]
null
Amiram Eldar, Mar 18 2023
2023-03-19T08:29:28
oeisdata/seq/A361/A361620.seq
df494f128789413e6ee417b23e8dff1c
A361621
Decimal expansion of the mode of the distribution of the least of the nine acute angles between pairs of edges of two randomly disoriented cubes (in radians).
[ "4", "0", "6", "8", "1", "1", "7", "8", "0", "1", "7", "4", "2", "0", "8", "7", "7", "1", "0", "1", "3", "8", "4", "2", "6", "8", "8", "1", "1", "8", "0", "8", "0", "8", "0", "3", "4", "4", "4", "4", "8", "6", "0", "9", "2", "9", "1", "3", "4", "6", "2", "7", "1", "7", "8", "7", "2", "0", "5", "0", "7", "9", "6", "3", "2", "3", "1", "9", "3", "8", "6", "4", "8", "8", "2", "0", "0", "7", "9", "5", "3", "9", "6", "7", "2", "4", "1", "0", "6", "1", "5", "7", "8", "6", "4", "6", "0", "3", "7", "0", "4", "7", "0", "8", "9" ]
[ "nonn", "cons" ]
7
0
1
[ "A228496", "A361601", "A361618", "A361619", "A361620", "A361621" ]
null
Amiram Eldar, Mar 18 2023
2023-03-18T06:54:53
oeisdata/seq/A361/A361621.seq
4957861bf7755c0eefdc957e1b6bfa1e
A361622
Number of distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes using only a compass.
[ "13", "46", "99", "164", "257", "370", "503", "648", "821", "1014", "1227", "1444", "1697", "1970", "2255" ]
[ "nonn", "more" ]
9
1
1
[ "A353782", "A354605", "A356358", "A361622", "A361623" ]
null
Scott R. Shannon, Mar 18 2023
2023-03-20T10:39:26
oeisdata/seq/A361/A361622.seq
43ed659da151394296333ae6aeb13c1e
A361623
Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes using only a compass.
[ "0", "40", "60", "12", "0", "484", "583", "160", "28", "8", "0", "2196", "2416", "804", "104", "28", "0", "5676", "6616", "2184", "460", "40", "8", "13456", "16936", "5236", "1340", "104", "12", "4", "27512", "35032", "11796", "2400", "320", "28", "0", "4", "0", "50688", "65044", "22536", "4632", "584", "60", "12", "4", "8", "84300", "105860", "38024", "8124", "1080", "108" ]
[ "nonn", "tabf" ]
10
1
2
[ "A353782", "A354605", "A356358", "A359061", "A359258", "A359619", "A359862", "A359935", "A361622", "A361623" ]
null
Scott R. Shannon, Mar 18 2023
2023-03-22T12:50:26
oeisdata/seq/A361/A361623.seq
88fd972e4a6fcad93cb8e41968f42e84
A361624
Number of distinct prime factors in decimal concatenation of integer (n, n-1, ..., 2, 1, 2, ..., n-1, n) = A007942(n).
[ "0", "2", "3", "2", "5", "3", "3", "4", "3", "3", "3", "3", "1", "4", "6", "2", "2", "3", "4", "7", "4", "8", "2", "3", "4", "6", "5", "7", "5", "6", "6", "3", "5", "7", "4", "5", "8", "5", "6", "6", "3", "3", "7", "7", "7", "7", "10", "7", "6", "6", "7", "4", "5", "5", "7" ]
[ "nonn", "base", "more" ]
30
1
2
[ "A001221", "A007942", "A110760", "A360736", "A361624" ]
null
Bernard Schott, Mar 18 2023
2023-10-16T22:28:30
oeisdata/seq/A361/A361624.seq
3d0b48c355741f8d57149e56102ed1aa
A361625
Number of free polyominoes with checkerboard-pattern-colored vertices with n cells.
[ "1", "1", "3", "7", "20", "60", "204", "702", "2526", "9180", "33989", "126713", "476597", "1802109", "6850969", "26151529", "100207548", "385217382", "1485216987", "5741240989", "22246000726", "86383317470", "336093551268", "1309997856337", "5114452295933", "19998171631076", "78306014924606", "307022177714062" ]
[ "nonn" ]
38
1
3
[ "A000105", "A001933", "A019988", "A122675", "A234008", "A346799", "A349328", "A351127", "A351142", "A351190", "A359689", "A361625", "A366766" ]
null
Andrey Zabolotskiy, Mar 19 2023; thanks to John Mason for his help.
2023-11-05T07:49:31
oeisdata/seq/A361/A361625.seq
df25f3ff82a0330272844ea8d2cf5d05
A361626
Expansion of e.g.f. exp( x/(1-x)^3 ) / (1-x)^2.
[ "1", "3", "17", "139", "1437", "17711", "252133", "4059567", "72779129", "1435276027", "30836352441", "716101686323", "17858449006357", "475653606922599", "13467411746316557", "403708230041927191", "12767545998797849073", "424670548932688771187", "14814998283177691422049" ]
[ "nonn" ]
17
0
2
[ "A000262", "A001339", "A091695", "A343884", "A351767", "A361599", "A361626" ]
null
Seiichi Manyama, Mar 18 2023
2023-03-29T04:44:33
oeisdata/seq/A361/A361626.seq
078fc82791837de65aa4994a9bcc7832
A361627
Positive integers such that GCD(A007504(n),n) != 1.
[ "18", "23", "24", "25", "30", "36", "42", "53", "54", "56", "57", "63", "78", "84", "85", "90", "99", "105", "111", "117", "123", "126", "129", "138", "154", "170", "177", "180", "190", "195", "207", "213", "222", "228", "230", "237", "238", "240", "245", "246", "252", "258", "270", "273", "275", "276", "282", "288", "297", "299", "303", "304", "309", "318", "319", "322", "327", "333", "339", "345" ]
[ "nonn" ]
18
1
1
[ "A007504", "A301274", "A361627" ]
null
Luca Onnis, Mar 18 2023
2023-03-22T15:18:08
oeisdata/seq/A361/A361627.seq
d4ce6b395f6f8edae96f59c5306c094a
A361628
Sphenic numbers (products of 3 distinct primes) whose digits are primes.
[ "222", "255", "273", "322", "357", "555", "777", "2222", "2233", "2235", "2255", "2337", "2355", "2373", "2522", "2553", "2555", "2737", "2755", "3237", "3322", "3333", "3335", "3355", "3522", "3535", "3553", "3723", "5222", "5235", "5253", "5322", "5335", "5522", "5523", "5555", "5727", "5735", "5757", "7222", "7257", "7322", "7337", "7527", "7535", "7553", "7557" ]
[ "nonn", "base" ]
15
1
1
[ "A007304", "A046034", "A102782", "A361628" ]
null
Massimo Kofler, Mar 18 2023
2023-04-23T23:19:35
oeisdata/seq/A361/A361628.seq
3ba30ec8a420c95d0872ce9fd57c038c
A361629
For n <= 2, a(n) = n. Thereafter let p be the greatest prime which divides the least number of terms in U = {a(n-2), a(n-1)}, then a(n) is the smallest multiple of p that is not yet in the sequence.
[ "1", "2", "4", "6", "3", "8", "9", "12", "10", "5", "14", "7", "16", "21", "28", "15", "35", "42", "20", "49", "56", "18", "63", "70", "25", "77", "11", "84", "22", "33", "24", "44", "55", "30", "66", "88", "27", "99", "110", "40", "121", "132", "36", "143", "13", "154", "26", "39", "45", "52", "65", "50", "78", "91", "98", "104", "117", "48", "130", "156", "60", "169", "182", "105", "195", "208", "75", "221", "17", "234", "34", "51", "54", "68", "85", "80", "102", "119", "112", "136", "153", "57", "19" ]
[ "nonn" ]
12
1
2
[ "A006094", "A007947", "A361133", "A361534", "A361629" ]
null
David James Sycamore, Mar 18 2023
2023-04-23T23:30:47
oeisdata/seq/A361/A361629.seq
c12d72919e7be65bb5e888562399620c
A361630
a(n) is the numerator of the median of the distinct prime factors of n.
[ "2", "3", "2", "5", "5", "7", "2", "3", "7", "11", "5", "13", "9", "4", "2", "17", "5", "19", "7", "5", "13", "23", "5", "5", "15", "3", "9", "29", "3", "31", "2", "7", "19", "6", "5", "37", "21", "8", "7", "41", "3", "43", "13", "4", "25", "47", "5", "7", "7", "10", "15", "53", "5", "8", "9", "11", "31", "59", "3", "61", "33", "5", "2", "9", "3", "67", "19", "13", "5", "71", "5", "73", "39", "4", "21", "9", "3" ]
[ "nonn", "frac" ]
16
2
1
[ "A001221", "A027748", "A323171", "A361565", "A361630", "A361631", "A361632" ]
null
Stefano Spezia, Mar 18 2023
2023-03-24T17:09:47
oeisdata/seq/A361/A361630.seq
50a9485b9009b8eb32d3c0820a9380cc
A361631
a(n) is the denominator of the median of the distinct prime factors of n.
[ "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1" ]
[ "nonn", "frac" ]
14
2
5
[ "A001221", "A027748", "A323172", "A361566", "A361630", "A361631", "A361633" ]
null
Stefano Spezia, Mar 18 2023
2023-03-23T23:09:03
oeisdata/seq/A361/A361631.seq
4aea838f9cf600f9153a06d01733e270
A361632
a(n) is the numerator of the median of the prime factors of n with repetition.
[ "2", "3", "2", "5", "5", "7", "2", "3", "7", "11", "2", "13", "9", "4", "2", "17", "3", "19", "2", "5", "13", "23", "2", "5", "15", "3", "2", "29", "3", "31", "2", "7", "19", "6", "5", "37", "21", "8", "2", "41", "3", "43", "2", "3", "25", "47", "2", "7", "5", "10", "2", "53", "3", "8", "2", "11", "31", "59", "5", "61", "33", "3", "2", "9", "3", "67", "2", "13", "5", "71", "2", "73", "39", "5", "2", "9", "3", "79" ]
[ "nonn", "frac" ]
11
2
1
[ "A001222", "A027746", "A079879", "A323171", "A361565", "A361630", "A361632", "A361633", "A361725" ]
null
Stefano Spezia, Mar 18 2023
2023-03-23T23:09:10
oeisdata/seq/A361/A361632.seq
580e5190bf7846211d1ddd5ad66a8e2c
A361633
a(n) is the denominator of the median of the prime factors of n with repetition.
[ "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1" ]
[ "nonn", "frac" ]
13
2
5
[ "A001222", "A027746", "A079879", "A323172", "A361566", "A361631", "A361632", "A361633", "A361725" ]
null
Stefano Spezia, Mar 18 2023
2024-08-04T10:14:05
oeisdata/seq/A361/A361633.seq
91c0115fb4e7ff9e6e50c38945c82229
A361634
Integers whose number of square divisors is coprime to the number of their nonsquare divisors.
[ "1", "2", "3", "4", "5", "6", "7", "9", "10", "11", "13", "14", "15", "16", "17", "19", "21", "22", "23", "25", "26", "29", "30", "31", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "46", "47", "48", "49", "51", "53", "55", "57", "58", "59", "61", "62", "64", "65", "66", "67", "69", "70", "71", "73", "74", "77", "78", "79", "80", "81", "82", "83", "85", "86", "87", "89", "91", "93", "94" ]
[ "nonn" ]
25
1
2
[ "A005117", "A046951", "A056595", "A210490", "A361634" ]
null
Waldemar Puszkarz, Mar 19 2023
2023-04-08T23:26:16
oeisdata/seq/A361/A361634.seq
aebe9ad798e519819fdafe78b4b4bd48
A361635
Number of strictly-convex unit-sided polygons with all internal angles equal to a multiple of Pi/n, ignoring rotational and reflectional copies.
[ "0", "1", "3", "4", "7", "16", "17", "28", "70", "85", "125", "392", "379", "704", "3359", "2248", "4111", "18510", "14309", "30820" ]
[ "nonn", "more" ]
19
1
3
[ "A164896", "A361635", "A361659" ]
null
Roman Mecholsky, Mar 18 2023
2023-04-28T16:23:19
oeisdata/seq/A361/A361635.seq
fff42f42a37b68995b335119990b1980
A361636
Diagonal of the rational function 1/(1 - v*w*x*y*z * (1 + 1/v + 1/w + 1/x + 1/y + 1/z)).
[ "1", "1", "1", "1", "121", "721", "2521", "6721", "128521", "1277641", "7539841", "32527441", "281835841", "3031468441", "23779315561", "139431015361", "962322302761", "9034098300361", "79726215362761", "569831799431881", "3952559737085401", "32660742079719601", "289694072383115401" ]
[ "nonn" ]
19
0
5
[ "A001850", "A008978", "A208425", "A274783", "A361636" ]
null
Seiichi Manyama, Mar 19 2023
2023-03-19T11:53:57
oeisdata/seq/A361/A361636.seq
38e49646ed3e1579914de1395296ea8f
A361637
Constant term in the expansion of (1 + x + y + z + 1/(x*y*z))^n.
[ "1", "1", "1", "1", "25", "121", "361", "841", "4201", "25705", "118441", "423721", "1628881", "8065201", "41225185", "184416961", "768211081", "3420474121", "16620237001", "79922011465", "364149052705", "1638806098945", "7655390077105", "36739991161105", "174363209490625", "811840219629121", "3790118889635521" ]
[ "nonn" ]
16
0
5
[ "A002426", "A008977", "A328725", "A344560", "A361637" ]
null
Seiichi Manyama, Mar 19 2023
2023-03-20T04:31:32
oeisdata/seq/A361/A361637.seq
63dae3f2edc89dfe02e667a972fb408e
A361638
Expansion of g.f. A(x) satisfying A(x) = 1 + x * A(x)^2 * (1 + A(x)^3).
[ "1", "2", "14", "142", "1690", "21994", "303126", "4348102", "64235570", "970695442", "14934154334", "233133082494", "3683546302538", "58794776161274", "946619511627622", "15355445768326710", "250717346336174690", "4117189670041072930", "67956239699290313646", "1126763233375565370990" ]
[ "nonn", "easy" ]
24
0
2
[ "A027307", "A219534", "A361638" ]
null
Seiichi Manyama, Jul 13 2023
2023-07-13T08:36:40
oeisdata/seq/A361/A361638.seq
ca8a0adfabac88a0b4afc874a8a3b96c
A361639
For n > 1, A359804(n) is a multiple of A361503(n-1); a(n) = A359804(n) / A361503(n-1).
[ "1", "1", "1", "2", "2", "2", "1", "3", "4", "3", "2", "1", "4", "4", "3", "2", "5", "6", "4", "6", "3", "5", "8", "8", "8", "6", "4", "9", "7", "13", "9", "10", "8", "12", "11", "9", "16", "12", "10", "6", "1", "13", "17", "13", "15", "19", "11", "16", "16", "12", "8", "17", "17", "23", "18", "13", "9", "26", "19", "18", "14", "20", "19", "15", "29", "10", "23", "16", "23", "24", "17", "24", "11", "18" ]
[ "nonn" ]
10
2
4
[ "A359804", "A361503", "A361639" ]
null
Rémy Sigrist, Mar 19 2023
2023-03-19T17:46:35
oeisdata/seq/A361/A361639.seq
e1018d51c7b581b826875f703e933ecd
A361640
a(0) = 0, a(1) = 1; thereafter let b be the least power of 2 that does not appear in the binary expansions of a(n-2) and a(n-1), then a(n) is the smallest multiple of b that is not yet in the sequence.
[ "0", "1", "2", "4", "3", "8", "12", "5", "6", "16", "7", "24", "32", "9", "10", "20", "11", "64", "28", "13", "14", "48", "15", "128", "80", "17", "18", "36", "19", "40", "44", "21", "22", "56", "23", "192", "72", "25", "26", "52", "27", "256", "60", "29", "30", "96", "31", "384", "160", "33", "34", "68", "35", "88", "76", "37", "38", "104", "39", "112", "120", "41", "42", "84", "43" ]
[ "nonn", "base" ]
17
0
3
[ "A006519", "A359804", "A361640", "A361641" ]
null
Rémy Sigrist, Mar 19 2023
2023-03-21T09:23:27
oeisdata/seq/A361/A361640.seq
bdc7784732451cb6a4f54ad6dc3720f6
A361641
Inverse permutation to A361640.
[ "0", "1", "2", "4", "3", "7", "8", "10", "5", "13", "14", "16", "6", "19", "20", "22", "9", "25", "26", "28", "15", "31", "32", "34", "11", "37", "38", "40", "18", "43", "44", "46", "12", "49", "50", "52", "27", "55", "56", "58", "29", "61", "62", "64", "30", "67", "68", "70", "21", "73", "74", "76", "39", "79", "80", "82", "33", "85", "86", "88", "42", "91", "92", "94", "17", "97", "98" ]
[ "nonn", "base" ]
9
0
3
[ "A361640", "A361641" ]
null
Rémy Sigrist, Mar 19 2023
2023-03-19T17:47:18
oeisdata/seq/A361/A361641.seq
52dce7c009fedbcddbcf952a5a6c4eba
A361642
Triangle read by rows where row n is a self-inverse permutation of 1..n formed starting from a column 1..n and sliding numbers to the right and down.
[ "1", "1", "2", "1", "3", "2", "1", "4", "3", "2", "1", "5", "3", "4", "2", "1", "6", "4", "3", "5", "2", "1", "7", "4", "3", "5", "6", "2", "1", "8", "5", "6", "3", "4", "7", "2", "1", "9", "5", "4", "3", "7", "6", "8", "2", "1", "10", "6", "4", "8", "3", "7", "5", "9", "2", "1", "11", "6", "8", "5", "3", "9", "4", "7", "10", "2", "1", "12", "7", "5", "4", "10", "3", "8", "9", "6", "11", "2", "1", "13", "7", "5", "4", "6", "3", "11", "10", "9", "8", "12", "2", "1", "14", "8", "10", "11", "6", "12", "3", "9", "4", "5", "7", "13", "2" ]
[ "nonn", "tabl" ]
56
1
3
[ "A000217", "A002260", "A002378", "A361642", "A361660" ]
null
Tamas Sandor Nagy, Mar 19 2023
2023-03-25T13:21:16
oeisdata/seq/A361/A361642.seq
3c72a828dc302e114348a2d6acae2ea7
A361643
The binary expansion of a(n) specifies which primes divide A359804(n).
[ "0", "1", "2", "4", "1", "3", "5", "8", "2", "1", "6", "9", "16", "3", "5", "10", "17", "4", "3", "9", "7", "18", "12", "1", "3", "5", "11", "17", "6", "8", "33", "2", "5", "9", "3", "20", "10", "1", "7", "13", "19", "32", "36", "65", "34", "6", "129", "24", "3", "5", "11", "17", "68", "66", "257", "7", "40", "18", "33", "132", "3", "9", "5", "130", "14", "513", "21", "258", "9", "260", "3", "72", "7" ]
[ "nonn", "base" ]
9
1
3
[ "A087207", "A359804", "A361643" ]
null
Rémy Sigrist, Mar 19 2023
2023-03-19T17:47:25
oeisdata/seq/A361/A361643.seq
65b81b1391e7c4c139f99f590510a525
A361644
Irregular triangle T(n, k), n >= 0, k = 1..max(1, 2^(A005811(n)-1)), read by rows; the n-th row lists the integers with the same binary length as n and whose partial sums of run lengths are included in those of n.
[ "0", "1", "2", "3", "3", "4", "7", "4", "5", "6", "7", "6", "7", "7", "8", "15", "8", "9", "14", "15", "8", "9", "10", "11", "12", "13", "14", "15", "8", "11", "12", "15", "12", "15", "12", "13", "14", "15", "14", "15", "15", "16", "31", "16", "17", "30", "31", "16", "17", "18", "19", "28", "29", "30", "31", "16", "19", "28", "31", "16", "19", "20", "23", "24", "27", "28", "31" ]
[ "nonn", "base", "tabf" ]
17
0
3
[ "A003817", "A005811", "A092339", "A101211", "A225081", "A342126", "A361644", "A361645", "A361646", "A361674", "A361676" ]
null
Rémy Sigrist, Mar 19 2023
2023-03-21T15:03:56
oeisdata/seq/A361/A361644.seq
261d6e4454abf4cf310281a93409dde6
A361645
a(n) is the least k such that n appears in the k-th row of triangle A361644.
[ "0", "1", "2", "2", "4", "5", "5", "4", "8", "9", "10", "10", "10", "10", "9", "8", "16", "17", "18", "18", "20", "21", "21", "20", "20", "21", "21", "20", "18", "18", "17", "16", "32", "33", "34", "34", "36", "37", "37", "36", "40", "41", "42", "42", "42", "42", "41", "40", "40", "41", "42", "42", "42", "42", "41", "40", "36", "37", "37", "36", "34", "34", "33", "32", "64", "65", "66", "66" ]
[ "nonn", "base" ]
14
0
3
[ "A000975", "A003714", "A101211", "A361645", "A361676" ]
null
Rémy Sigrist, Mar 19 2023
2023-03-21T15:04:20
oeisdata/seq/A361/A361645.seq
6e4943aa738eb7351031b6df5c4eb7e9
A361646
Distinct values of A361644, in order of appearance.
[ "0", "1", "2", "3", "4", "7", "5", "6", "8", "15", "9", "14", "10", "11", "12", "13", "16", "31", "17", "30", "18", "19", "28", "29", "20", "23", "24", "27", "21", "22", "25", "26", "32", "63", "33", "62", "34", "35", "60", "61", "36", "39", "56", "59", "37", "38", "57", "58", "40", "47", "48", "55", "41", "46", "49", "54", "42", "43", "44", "45", "50", "51", "52", "53", "64", "127", "65" ]
[ "nonn", "base" ]
9
0
3
[ "A361644", "A361646", "A361647" ]
null
Rémy Sigrist, Mar 19 2023
2023-03-21T15:03:48
oeisdata/seq/A361/A361646.seq
b650bd0f32b7c68265d4b816976f305b
A361647
Inverse permutation to A361646.
[ "0", "1", "2", "3", "4", "6", "7", "5", "8", "10", "12", "13", "14", "15", "11", "9", "16", "18", "20", "21", "24", "28", "29", "25", "26", "30", "31", "27", "22", "23", "19", "17", "32", "34", "36", "37", "40", "44", "45", "41", "48", "52", "56", "57", "58", "59", "53", "49", "50", "54", "60", "61", "62", "63", "55", "51", "42", "46", "47", "43", "38", "39", "35", "33", "64", "66", "68", "69" ]
[ "nonn", "base" ]
9
0
3
[ "A361646", "A361647" ]
null
Rémy Sigrist, Mar 19 2023
2023-03-21T15:03:51
oeisdata/seq/A361/A361647.seq
ae4c76f1d2856b6dd271d78fc826e6e3
A361648
Number of permutations p of [n] such that p(i), p(i+2), p(i+4),... form an up-down sequence for i in {1,2}.
[ "1", "1", "2", "3", "6", "20", "80", "350", "1750", "10080", "64512", "450912", "3438204", "28471872", "253913088", "2424193200", "24687555750", "267199961600", "3062092267520", "37037541651968", "471565937953396", "6304419553216512", "88298062293762048", "1292879475255280640", "19753693667117055100" ]
[ "nonn" ]
28
0
3
[ "A000111", "A000142", "A001405", "A361648", "A361651" ]
null
Alois P. Heinz, Mar 19 2023
2023-12-06T14:44:21
oeisdata/seq/A361/A361648.seq
d9a71f21bece0943bba104982473afba
A361649
a(n) = (1+n)*(2*a(n-1) - (n-2)*a(n-2)) with a(0) = a(1) = 1.
[ "1", "1", "6", "44", "380", "3768", "42112", "523072", "7141248", "106209920", "1708188416", "29525850624", "545607622144", "10730032423936", "223691600732160", "4926284479250432", "114255071320260608", "2783085758131765248", "71023717127647854592", "1894699527341113999360", "52730415074075898937344" ]
[ "nonn" ]
41
0
3
[ "A052852", "A288268", "A361528", "A361649" ]
null
Igor Victorovich Statsenko, Mar 19 2023
2024-02-25T10:08:19
oeisdata/seq/A361/A361649.seq
4e00ac1bcb9e2e2b52f610ae014370cd
A361650
Irregular triangle read by rows in which the row n lists the prime factors of n having the highest multiplicity.
[ "2", "3", "2", "5", "2", "3", "7", "2", "3", "2", "5", "11", "2", "13", "2", "7", "3", "5", "2", "17", "3", "19", "2", "3", "7", "2", "11", "23", "2", "5", "2", "13", "3", "2", "29", "2", "3", "5", "31", "2", "3", "11", "2", "17", "5", "7", "2", "3", "37", "2", "19", "3", "13", "2", "41", "2", "3", "7", "43", "2", "3", "2", "23", "47", "2", "7", "5", "3", "17", "2", "53", "3", "5", "11", "2", "3", "19", "2", "29", "59" ]
[ "nonn", "tabf" ]
22
2
1
[ "A001221", "A001222", "A027746", "A051903", "A356838", "A356840", "A361632", "A361633", "A361650" ]
null
Stefano Spezia, Mar 19 2023
2023-03-24T07:59:29
oeisdata/seq/A361/A361650.seq
44f032a5f28fb7c9678b09538781be20
A361651
Number T(n,k) of permutations p of [n] such that p(i), p(i+k), p(i+2k),... form an up-down sequence for i in [k]; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
[ "1", "0", "1", "0", "1", "2", "0", "2", "3", "6", "0", "5", "6", "12", "24", "0", "16", "20", "30", "60", "120", "0", "61", "80", "90", "180", "360", "720", "0", "272", "350", "420", "630", "1260", "2520", "5040", "0", "1385", "1750", "2240", "2520", "5040", "10080", "20160", "40320", "0", "7936", "10080", "13440", "15120", "22680", "45360", "90720", "181440", "362880" ]
[ "nonn", "look", "tabl" ]
23
0
6
[ "A000007", "A000111", "A000142", "A000680", "A248686", "A333706", "A361648", "A361651", "A367336" ]
null
Alois P. Heinz, Mar 19 2023
2023-12-06T14:44:03
oeisdata/seq/A361/A361651.seq
a58d700fed6a5523c289035ea6d1ba11
A361652
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/2)} k^j * Stirling2(n-j,j)/(n-j)!.
[ "1", "1", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "4", "3", "0", "1", "0", "6", "6", "16", "0", "1", "0", "8", "9", "56", "65", "0", "1", "0", "10", "12", "120", "250", "336", "0", "1", "0", "12", "15", "208", "555", "1812", "1897", "0", "1", "0", "14", "18", "320", "980", "5148", "12614", "11824", "0", "1", "0", "16", "21", "456", "1525", "11064", "39711", "101040", "80145", "0" ]
[ "nonn", "tabl" ]
30
0
9
[ "A000007", "A052506", "A290158", "A351733", "A351734", "A361652", "A362834" ]
null
Seiichi Manyama, May 05 2023
2023-05-05T12:25:05
oeisdata/seq/A361/A361652.seq
69a29bd7bb90a3ba142186708fc9e678
A361653
Number of even-length integer partitions of n with integer median.
[ "0", "0", "1", "0", "3", "1", "5", "3", "11", "7", "17", "16", "32", "31", "52", "55", "90", "99", "144", "167", "236", "273", "371", "442", "587", "696", "901", "1078", "1379", "1651", "2074", "2489", "3102", "3707", "4571", "5467", "6692", "7982", "9696", "11543", "13949", "16563", "19891", "23572", "28185", "33299", "39640", "46737", "55418", "65164" ]
[ "nonn" ]
10
0
5
[ "A000009", "A000041", "A000975", "A008284", "A013580", "A027193", "A051293", "A067538", "A067659", "A079309", "A240219", "A240850", "A307683", "A325347", "A349156", "A359893", "A359897", "A359901", "A359902", "A359908", "A359912", "A360005", "A360952", "A361653", "A361655" ]
null
Gus Wiseman, Mar 23 2023
2023-03-24T17:01:04
oeisdata/seq/A361/A361653.seq
59fb68b605666e8ec6799c3a0d4039b4
A361654
Triangle read by rows where T(n,k) is the number of nonempty subsets of {1,...,2n-1} with median n and minimum k.
[ "1", "2", "1", "5", "3", "1", "15", "9", "4", "1", "50", "29", "14", "5", "1", "176", "99", "49", "20", "6", "1", "638", "351", "175", "76", "27", "7", "1", "2354", "1275", "637", "286", "111", "35", "8", "1", "8789", "4707", "2353", "1078", "441", "155", "44", "9", "1", "33099", "17577", "8788", "4081", "1728", "650", "209", "54", "10", "1" ]
[ "nonn", "tabl" ]
21
1
2
[ "A000975", "A006134", "A007318", "A013580", "A024718", "A057552", "A067659", "A079309", "A231147", "A325347", "A327475", "A327481", "A359893", "A359901", "A359907", "A360005", "A361654", "A361849" ]
null
Gus Wiseman, Mar 23 2023
2025-02-19T12:11:52
oeisdata/seq/A361/A361654.seq
c4be81663fe0eee71658d226b1feee10
A361655
Number of even-length integer partitions of 2n with integer mean.
[ "0", "1", "3", "4", "10", "6", "33", "8", "65", "68", "117", "12", "583", "14", "319", "1078", "1416", "18", "3341", "20", "8035", "5799", "1657", "24", "36708", "16954", "3496", "24553", "68528", "30", "192180", "32", "178802", "91561", "14625", "485598", "955142", "38", "29223", "316085", "2622697", "42", "3528870", "44", "2443527", "5740043" ]
[ "nonn" ]
12
0
3
[ "A000009", "A000016", "A000041", "A000975", "A008284", "A027187", "A027193", "A051293", "A058398", "A067538", "A067659", "A082550", "A102627", "A236913", "A237984", "A240219", "A307683", "A316413", "A325347", "A326567", "A326568", "A326622", "A327475", "A327482", "A348551", "A359893", "A361653", "A361655", "A361656" ]
null
Gus Wiseman, Mar 23 2023
2023-03-24T17:58:56
oeisdata/seq/A361/A361655.seq
bc355aaf26ce54d2dd31dde740abf3d6
A361656
Number of odd-length integer partitions of n with integer mean.
[ "0", "1", "1", "2", "1", "2", "4", "2", "1", "9", "8", "2", "13", "2", "16", "51", "1", "2", "58", "2", "85", "144", "57", "2", "49", "194", "102", "381", "437", "2", "629", "2", "1", "956", "298", "2043", "1954", "2", "491", "2293", "1116", "2", "4479", "2", "6752", "14671", "1256", "2", "193", "8035", "4570", "11614", "22143", "2", "28585", "39810", "16476", "24691", "4566" ]
[ "nonn" ]
11
0
4
[ "A000009", "A000016", "A000041", "A000975", "A008284", "A027187", "A027193", "A051293", "A058398", "A067538", "A067659", "A082550", "A102627", "A236559", "A236913", "A237984", "A240219", "A307683", "A316413", "A325347", "A326567", "A326568", "A326622", "A327475", "A327482", "A348551", "A361653", "A361655", "A361656" ]
null
Gus Wiseman, Mar 24 2023
2023-03-24T17:46:39
oeisdata/seq/A361/A361656.seq
5d56bf5524625e7ef781378ee00bb778
A361657
Constant term in the expansion of (1 + x^2 + y^2 + 1/(x*y))^n.
[ "1", "1", "1", "1", "13", "61", "181", "421", "1261", "5293", "21421", "73261", "232321", "789361", "2954953", "11127481", "39961741", "139908301", "499315501", "1835933293", "6792310153", "24827506873", "90058277233", "328509505633", "1210097040769", "4473191880961", "16495696956961", "60721903812961" ]
[ "nonn" ]
21
0
5
[ "A000897", "A002426", "A344560", "A361637", "A361657", "A361658" ]
null
Seiichi Manyama, Mar 19 2023
2023-03-20T07:32:44
oeisdata/seq/A361/A361657.seq
d9b49b0717afc6b71f9f9846b3073c58
A361658
Constant term in the expansion of (1 + x^3 + y^3 + z^3 + 1/(x*y*z))^n.
[ "1", "1", "1", "1", "1", "1", "121", "841", "3361", "10081", "25201", "55441", "194041", "1287001", "7927921", "38438401", "152312161", "516079201", "1627691521", "5745472321", "25999820401", "133086258481", "651284938921", "2860955078521", "11312609403481", "42039298455001", "158864460354601", "658342633033801" ]
[ "nonn" ]
20
0
7
[ "A001421", "A002426", "A361637", "A361657", "A361658" ]
null
Seiichi Manyama, Mar 19 2023
2023-03-20T07:32:34
oeisdata/seq/A361/A361658.seq
24417c46985f92552a405bce66d41056
A361659
Number of strictly convex unit-sided polygons with all internal angles equal to a multiple of Pi/n, treating polygons that have a unique mirror image as distinct but ignoring rotational copies.
[ "0", "1", "3", "4", "7", "17", "19", "34", "92", "115", "187", "616", "631", "1201", "6067", "4114", "7711", "35322", "27595", "59704", "328833", "190933", "364723", "2435778", "1579882", "2582059", "21013768", "9894292", "18512791", "377367013", "69273667", "134219794", "1678410949", "505301839", "1339499035", "14843799550" ]
[ "nonn" ]
7
1
3
[ "A164896", "A262181", "A361635", "A361659" ]
null
Roman Mecholsky, Mar 19 2023
2023-04-28T16:22:21
oeisdata/seq/A361/A361659.seq
b533a2ecec76fb12efde92b94d35b584
A361660
Irregular triangle read by rows where row n lists the successive numbers moved in the process of forming row n of the triangle A361642.
[ "2", "3", "2", "4", "3", "3", "2", "5", "4", "3", "4", "2", "6", "5", "4", "4", "3", "3", "5", "2", "7", "6", "5", "4", "5", "3", "5", "6", "2", "8", "7", "6", "5", "5", "4", "6", "3", "3", "4", "7", "2", "9", "8", "7", "6", "5", "6", "4", "4", "7", "3", "7", "6", "8", "2", "10", "9", "8", "7", "6", "6", "5", "7", "4", "7", "8", "3", "3", "7", "5", "9", "2", "11", "10", "9", "8", "7", "6", "7", "5", "8", "4", "5", "9", "3", "9", "4", "7", "10", "2" ]
[ "nonn", "tabf" ]
46
1
1
[ "A002541", "A361642", "A361660" ]
null
Tamas Sandor Nagy, Mar 19 2023
2023-04-13T08:30:50
oeisdata/seq/A361/A361660.seq
4a6107b51ed5d619fe4e91ff0aca1658
A361661
Number of Q-isomorphism classes of elliptic curves E/Q with good reduction outside the first n prime numbers.
[ "0", "24", "752", "7600", "71520", "592192" ]
[ "nonn", "more" ]
56
0
2
[ "A332545", "A359480", "A361661" ]
null
Robin Visser, Mar 21 2023
2023-04-12T08:07:12
oeisdata/seq/A361/A361661.seq
3646945e7b774974c0b2f7fbeb447a9c
A361662
Least number k >= 1 such that A074206(k) is divisible by n.
[ "1", "4", "6", "8", "24", "48", "96", "12", "216", "24", "60", "48", "30", "96", "210", "32", "288", "216", "72", "24", "216", "60", "240", "48", "210", "36", "6480", "96", "15552", "4320", "7560", "64", "120", "288", "2520", "216", "5040", "72", "960", "768", "2520", "216", "576", "60", "83160", "240", "7680", "48", "18480", "13860", "7776", "144", "1152", "6480" ]
[ "nonn" ]
15
1
2
[ "A025487", "A074206", "A361662", "A361663", "A361664", "A361666" ]
null
Pontus von Brömssen, Mar 20 2023
2023-07-15T14:55:37
oeisdata/seq/A361/A361662.seq
c2bcb204849e053e0cb8269e178b6964
A361663
A361662(n) = A025487(a(n)).
[ "1", "3", "4", "5", "8", "12", "16", "6", "23", "8", "13", "12", "9", "16", "22", "10", "26", "23", "15", "8", "23", "13", "24", "12", "22", "11", "73", "16", "97", "64", "77", "14", "17", "26", "55", "23", "67", "15", "39", "35", "55", "23", "33", "13", "154", "24", "78", "12", "101", "93", "79", "19", "42", "73", "93", "16", "99", "97", "34", "64", "31", "77", "23", "18", "93", "17", "77" ]
[ "nonn" ]
4
1
2
[ "A025487", "A361662", "A361663" ]
null
Pontus von Brömssen, Mar 20 2023
2023-03-24T17:44:49
oeisdata/seq/A361/A361663.seq
e0931a69282613b566eb64921c2ee8a6
A361664
a(n) = A074206(A361662(n))/n.
[ "1", "1", "1", "1", "4", "8", "16", "1", "28", "2", "4", "4", "1", "8", "5", "1", "32", "14", "4", "1", "12", "2", "16", "2", "3", "1", "1104", "4", "2944", "848", "804", "1", "4", "16", "164", "7", "544", "2", "64", "32", "140", "6", "32", "1", "6812", "8", "768", "1", "752", "286", "528", "4", "64", "552", "260", "2", "3904", "1472", "32", "424", "16", "402", "4", "1", "220", "2", "372", "8" ]
[ "nonn" ]
7
1
5
[ "A074206", "A361662", "A361664", "A361667", "A361668" ]
null
Pontus von Brömssen, Mar 20 2023
2023-03-24T17:44:57
oeisdata/seq/A361/A361664.seq
ac89684ac2b08b89a3a6d0069b63f9d7
A361665
Number of ordered factorizations of p_1^x_1 * ... * p_k^x_k, where (x_1, ..., x_k) is the partition with Heinz number n and p_1, ..., p_k are distinct primes.
[ "1", "1", "2", "3", "4", "8", "8", "13", "26", "20", "16", "44", "32", "48", "76", "75", "64", "176", "128", "132", "208", "112", "256", "308", "252", "256", "818", "368", "512", "604", "1024", "541", "544", "576", "768", "1460", "2048", "1280", "1376", "1076", "4096", "1888", "8192", "976", "3172", "2816", "16384", "2612", "2568", "2316", "3392", "2496", "32768" ]
[ "nonn" ]
7
1
3
[ "A074206", "A181821", "A361665", "A361666" ]
null
Pontus von Brömssen, Mar 20 2023
2023-03-24T17:45:14
oeisdata/seq/A361/A361665.seq
3bc172e45a1bdae4bc5bd2cf75ca15cb
A361666
Least number k >= 1 such that A361665(k) is divisible by n.
[ "1", "3", "4", "5", "10", "14", "22", "6", "25", "10", "12", "14", "8", "22", "16", "11", "33", "25", "15", "10", "25", "12", "28", "14", "16", "9", "98", "22", "143", "75", "100", "13", "20", "33", "60", "25", "84", "15", "52", "38", "60", "25", "39", "12", "200", "28", "92", "14", "112", "72", "80", "21", "51", "98", "72", "22", "170", "143", "42", "75", "44", "100", "25", "17", "72" ]
[ "nonn" ]
4
1
2
[ "A361662", "A361665", "A361666", "A361667" ]
null
Pontus von Brömssen, Mar 20 2023
2023-03-24T17:45:38
oeisdata/seq/A361/A361666.seq
f985fb733dc3812aadafd94f2df17d4a
A361667
a(n) = A361665(A361666(n))/n.
[ "1", "1", "1", "1", "4", "8", "16", "1", "28", "2", "4", "4", "1", "8", "5", "1", "32", "14", "4", "1", "12", "2", "16", "2", "3", "1", "1104", "4", "2944", "454", "804", "1", "4", "16", "164", "7", "544", "2", "64", "32", "140", "6", "32", "1", "6812", "8", "768", "1", "752", "286", "204", "4", "64", "552", "260", "2", "3904", "1472", "32", "227", "16", "402", "4", "1", "220", "2", "372", "8" ]
[ "nonn" ]
5
1
5
[ "A361664", "A361665", "A361666", "A361667", "A361668" ]
null
Pontus von Brömssen, Mar 20 2023
2023-03-24T17:45:48
oeisdata/seq/A361/A361667.seq
3ec06758a5ec18e811587f17c27933e3
A361668
Numbers k such that A361662(k) != A181821(A361666(k)).
[ "30", "51", "60", "89", "102", "105", "113", "119", "120", "128", "135", "145", "149", "150", "153", "168", "178", "179", "181", "191", "200", "204", "210", "215", "219", "221", "224", "226", "238", "240", "245", "248", "256", "257", "267", "270", "277", "281", "290", "298", "299", "300", "305", "306", "313", "317", "323", "336", "343", "345", "349", "356", "357" ]
[ "nonn" ]
6
1
1
[ "A181820", "A181821", "A361662", "A361663", "A361666", "A361668" ]
null
Pontus von Brömssen, Mar 20 2023
2023-03-24T17:46:10
oeisdata/seq/A361/A361668.seq
cefb82fbc5a35ee5d4e1f1cb848b05cf
A361669
a(n) = floor of sinh(sinh(sinh(...(1)...))) with n iterations.
[ "1", "1", "1", "2", "3", "22", "3355531547" ]
[ "nonn", "easy" ]
14
0
4
[ "A000471", "A073742", "A361669" ]
null
Sylvia Zevi Abrams, Mar 20 2023
2023-04-09T17:56:51
oeisdata/seq/A361/A361669.seq
fbc318a6651941eca0c673b71a331164
A361670
Squarefree part of the n-th triangular number.
[ "1", "3", "6", "10", "15", "21", "7", "1", "5", "55", "66", "78", "91", "105", "30", "34", "17", "19", "190", "210", "231", "253", "69", "3", "13", "39", "42", "406", "435", "465", "31", "33", "561", "595", "70", "74", "703", "741", "195", "205", "861", "903", "946", "110", "115", "1081", "282", "6", "1", "51", "1326", "1378", "159", "165", "385", "399", "1653", "1711", "1770", "1830", "1891", "217", "14", "130", "2145", "2211", "2278" ]
[ "nonn", "easy" ]
14
1
2
[ "A000217", "A001108", "A007913", "A039963", "A083481", "A361670", "A361671" ]
null
R. J. Mathar, Mar 20 2023
2023-03-23T03:45:18
oeisdata/seq/A361/A361670.seq
26ef6e55396f373db2f06e7beeaede62
A361671
Squarefree part of the n-th tetrahedral number.
[ "1", "1", "10", "5", "35", "14", "21", "30", "165", "55", "286", "91", "455", "35", "170", "51", "969", "285", "1330", "385", "1771", "506", "23", "26", "13", "91", "406", "1015", "4495", "310", "341", "374", "6545", "1785", "7770", "2109", "9139", "2470", "2665", "2870", "12341", "3311", "14190", "3795", "16215", "1081", "94", "1", "17", "221", "23426", "689", "2915", "770", "7315", "7714", "32509", "8555" ]
[ "nonn", "easy" ]
10
1
3
[ "A000292", "A003556", "A007913", "A083481", "A361670", "A361671" ]
null
R. J. Mathar, Mar 20 2023
2023-03-23T03:45:11
oeisdata/seq/A361/A361671.seq
8e7988c9db34282c03b39fae3dc72302
A361672
a(1) = a(2) = 1; for n > 2, a(n) = a(n-2) + a(n-1) + n if a(n-1) and n are coprime, otherwise a(n) = a(n-1)/gcd(a(n-1), n).
[ "1", "1", "5", "10", "2", "1", "10", "5", "24", "12", "47", "71", "131", "216", "72", "9", "98", "49", "166", "83", "270", "135", "428", "107", "560", "280", "867", "1175", "2071", "3276", "5378", "2689", "8100", "4050", "810", "45", "892", "446", "1377", "1863", "3281", "5186", "8510", "4255", "851", "37", "935", "1020", "2004", "1002", "334", "167", "554", "277", "886" ]
[ "nonn", "easy" ]
7
1
3
[ "A091508", "A133058", "A133579", "A133580", "A255051", "A255140", "A361672" ]
null
Hubert W. Westwood, Mar 20 2023
2023-03-25T15:28:36
oeisdata/seq/A361/A361672.seq
b0de02dfa59b4b243f4f6b11d7aa85aa
A361673
Constant term in the expansion of (1 + x*y + y*z + z*x + 1/(x*y*z))^n.
[ "1", "1", "1", "1", "1", "61", "361", "1261", "3361", "7561", "34021", "235621", "1294921", "5482621", "19039021", "65345281", "286147681", "1511480881", "7688794681", "34337600281", "138221512741", "554603041441", "2454508134541", "11874549049441", "57412094595241", "261925516443361", "1134301869703861" ]
[ "nonn" ]
18
0
6
[ "A001460", "A344560", "A361637", "A361658", "A361673", "A361675" ]
null
Seiichi Manyama, Mar 20 2023
2023-03-22T07:55:13
oeisdata/seq/A361/A361673.seq
d789e70596b41dc79efefb3d4d0c244d
A361674
Irregular triangle T(n, k), n >= 0, k = 1..2^A092339(n), read by rows; the n-th row lists the numbers k such that n appears in the k-th row of A361644.
[ "0", "1", "2", "2", "3", "4", "5", "5", "5", "6", "4", "5", "6", "7", "8", "9", "10", "11", "9", "10", "10", "10", "11", "10", "11", "12", "13", "10", "13", "9", "10", "13", "14", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "17", "18", "21", "22", "18", "21", "18", "19", "20", "21", "20", "21", "21", "21", "22", "20", "21", "22", "23", "20", "21", "22", "23", "24", "25", "26", "27" ]
[ "nonn", "base", "tabf" ]
11
0
3
[ "A361644", "A361645", "A361674", "A361676" ]
null
Rémy Sigrist, Mar 20 2023
2023-03-21T15:03:39
oeisdata/seq/A361/A361674.seq
f402411db9cfe823c7b5895e48a7f6cf
A361675
Constant term in the expansion of (1 + x*y*z + w*y*z + w*x*z + w*x*y + 1/(w*x*y*z))^n.
[ "1", "1", "1", "1", "1", "1", "1", "841", "6721", "30241", "100801", "277201", "665281", "1441441", "10450441", "118918801", "917716801", "5162277121", "23183465761", "88037913601", "293383742401", "988690080001", "4810025534161", "33669381872281", "234722545854721", "1407984124932001", "7219196588604001" ]
[ "nonn" ]
21
0
8
[ "A344560", "A361673", "A361675" ]
null
Seiichi Manyama, Mar 20 2023
2023-03-22T07:52:56
oeisdata/seq/A361/A361675.seq
40a12508481d0f7c508925e64e9d516a
A361676
a(n) is the greatest k such that n appears in the k-th row of triangle A361644.
[ "0", "1", "2", "3", "5", "5", "6", "7", "11", "10", "10", "11", "13", "13", "14", "15", "23", "22", "21", "21", "21", "21", "22", "23", "27", "26", "26", "27", "29", "29", "30", "31", "47", "46", "45", "45", "43", "42", "42", "43", "43", "42", "42", "43", "45", "45", "46", "47", "55", "54", "53", "53", "53", "53", "54", "55", "59", "58", "58", "59", "61", "61", "62", "63", "95", "94", "93" ]
[ "nonn", "base" ]
12
0
3
[ "A000975", "A003754", "A101211", "A361644", "A361645", "A361676" ]
null
Rémy Sigrist, Mar 20 2023
2023-03-22T12:48:00
oeisdata/seq/A361/A361676.seq
491d9aa252ade6e039f3aee7975e38fc
A361677
Constant term in the expansion of (1 + x + y + z + 1/(x*y) + 1/(y*z) + 1/(z*x))^n.
[ "1", "1", "1", "19", "73", "181", "1711", "10081", "38809", "256033", "1696861", "8388271", "49449511", "326195299", "1847392093", "10789655059", "69202030969", "418647580489", "2498113460881", "15735859252147", "97919649290053", "598317173139313", "3748943081117323" ]
[ "nonn" ]
10
0
4
[ "A201805", "A275047", "A344560", "A361677", "A361678" ]
null
Seiichi Manyama, Mar 20 2023
2023-03-22T06:36:11
oeisdata/seq/A361/A361677.seq
a58bb1152cbba340205e958260c83e2c
A361678
Constant term in the expansion of (1 + w + x + y + z + 1/(x*y*z) + 1/(w*y*z) + 1/(w*x*z) + 1/(w*x*y))^n.
[ "1", "1", "1", "1", "97", "481", "1441", "3361", "77281", "647137", "3195361", "11674081", "116286721", "1147935361", "7611379777", "37451144641", "263670781921", "2456043418081", "19073086806241", "115319128034017", "748239468100417", "6179458007222977", "50636218964639617", "350400618132423937" ]
[ "nonn" ]
12
0
5
[ "A201805", "A361637", "A361677", "A361678" ]
null
Seiichi Manyama, Mar 20 2023
2023-03-22T06:52:12
oeisdata/seq/A361/A361678.seq
52d19e3fd6eb43ed9f4a8dd6899c1223
A361679
A(n,k) is the n-th prime p such that p + 2^k is also prime; square array A(n,k), n>=1, k>=1, read by antidiagonals.
[ "3", "3", "5", "3", "7", "11", "3", "5", "13", "17", "5", "7", "11", "19", "29", "3", "11", "13", "23", "37", "41", "3", "7", "29", "31", "29", "43", "59", "7", "11", "19", "41", "37", "53", "67", "71", "11", "13", "23", "37", "47", "43", "59", "79", "101", "7", "29", "37", "29", "43", "71", "67", "71", "97", "107", "5", "37", "59", "61", "53", "67", "107", "73", "89", "103", "137" ]
[ "nonn", "look", "tabl" ]
15
1
1
[ "A000040", "A001359", "A023200", "A023202", "A049488", "A049489", "A049490", "A049491", "A056206", "A361483", "A361484", "A361485", "A361679", "A361680" ]
null
Alois P. Heinz, Mar 20 2023
2023-03-20T13:35:19
oeisdata/seq/A361/A361679.seq
9b32706d82cf47d717385f5baa3c2ce9
A361680
The n-th prime p such that p + 2^n is also prime.
[ "3", "7", "11", "31", "47", "67", "83", "163", "179", "193", "263", "367", "389", "499", "563", "571", "887", "967", "1229", "1087", "1367", "1873", "1289", "2647", "1907", "2083", "1979", "2557", "2267", "3697", "2909", "3121", "3761", "4507", "4373", "4723", "5279", "5857", "6359", "6793", "7727", "8167", "7853", "6823", "6779", "8059", "9479", "10567" ]
[ "nonn" ]
10
1
1
[ "A000040", "A361679", "A361680" ]
null
Alois P. Heinz, Mar 20 2023
2023-03-22T08:17:16
oeisdata/seq/A361/A361680.seq
6044c75e2ca7778b3423d15a917f2b0f
A361681
Triangle read by rows. T(n, k) is the number of Fibonacci meanders with a central angle of 360/m degrees that make m*k left turns and whose length is m*n, where m = 3.
[ "1", "2", "1", "5", "2", "1", "10", "8", "2", "1", "17", "40", "8", "2", "1", "26", "161", "44", "8", "2", "1", "37", "506", "263", "44", "8", "2", "1", "50", "1312", "1466", "268", "44", "8", "2", "1", "65", "2948", "6812", "1726", "268", "44", "8", "2", "1", "82", "5945", "26048", "11062", "1732", "268", "44", "8", "2", "1", "101", "11026", "84149", "64548", "11617", "1732", "268", "44", "8", "2", "1" ]
[ "nonn", "tabl" ]
14
1
2
[ "A141147", "A202409", "A361574", "A361681" ]
null
Peter Luschny, Mar 20 2023
2023-03-31T06:52:41
oeisdata/seq/A361/A361681.seq
0dc69a27233feddfd3be0f986f0eefa3
A361682
Array read by descending antidiagonals. A(n, k) is the number of multiset combinations of {0, 1} whose type is defined in the comments. Also A(n, k) = hypergeom([-k, -2], [1], n).
[ "1", "1", "1", "1", "3", "1", "1", "6", "5", "1", "1", "10", "13", "7", "1", "1", "15", "25", "22", "9", "1", "1", "21", "41", "46", "33", "11", "1", "1", "28", "61", "79", "73", "46", "13", "1", "1", "36", "85", "121", "129", "106", "61", "15", "1", "1", "45", "113", "172", "201", "191", "145", "78", "17", "1", "1", "55", "145", "232", "289", "301", "265", "190", "97", "19", "1" ]
[ "nonn", "tabl" ]
16
0
5
[ "A000012", "A000217", "A001844", "A005408", "A028872", "A038764", "A069133", "A077028", "A081585", "A081587", "A081589", "A081591", "A100536", "A239325", "A239331", "A239592", "A361043", "A361045", "A361521", "A361682", "A361731" ]
null
Peter Luschny, Mar 21 2023
2023-03-23T07:57:37
oeisdata/seq/A361/A361682.seq
19bbc8138f6e2c676a28b349582d860d
A361683
a(n) is the least k such that tau(k) divides sigma_n(k) but not sigma(k), or -1 if no such k exists.
[ "4", "64", "4", "7168", "4", "606528", "4", "64", "4", "4194304", "4" ]
[ "nonn", "more" ]
48
2
1
[ "A000005", "A000203", "A001157", "A001158", "A003601", "A010709", "A020486", "A020639", "A046839", "A046840", "A361683" ]
null
Mohammed Yaseen, Mar 20 2023
2023-03-22T15:17:55
oeisdata/seq/A361/A361683.seq
83e84282f10465f3681165f56d8f3e42
A361684
Ramsey core number rc(n,n).
[ "2", "5", "8", "11", "15", "18", "22", "25", "28", "32", "35", "39", "42", "45", "49", "52", "56", "59", "62", "66", "69", "73", "76", "80", "83", "86", "90", "93", "97", "100", "103", "107", "110", "114", "117", "121", "124", "127", "131", "134", "138", "141", "144", "148", "151", "155", "158", "161", "165", "168", "172", "175", "179", "182", "185", "189", "192", "196", "199", "202" ]
[ "nonn", "tabl" ]
24
1
1
[ "A080036", "A361261", "A361684" ]
null
Allan Bickle, Mar 28 2023
2024-02-18T02:08:55
oeisdata/seq/A361/A361684.seq
beb58559afa59824ee9a2a9110fff472
A361685
Number of iterations of sopf until reaching a prime.
[ "0", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "2", "2", "1", "0", "1", "0", "1", "2", "1", "0", "1", "1", "3", "1", "2", "0", "2", "0", "1", "3", "1", "2", "1", "0", "3", "2", "1", "0", "2", "0", "1", "2", "2", "0", "1", "1", "1", "2", "3", "0", "1", "2", "2", "2", "1", "0", "2", "0", "4", "2", "1", "2", "2", "0", "1", "4", "3", "0", "1", "0", "3", "2", "3", "2", "2", "0", "1", "1", "1", "0", "2", "2", "3", "2", "1", "0", "2", "2", "2", "2", "2", "2", "1", "0", "2", "3", "1", "0" ]
[ "nonn" ]
21
2
13
[ "A008472", "A321944", "A361685" ]
null
J. W. Montgomery, Mar 29 2023
2025-01-28T15:30:14
oeisdata/seq/A361/A361685.seq
bbb92ce05de092b3c2def2a890c0aef0
A361686
a(n) is the least totient divisor of A329872(n), where A329872 are nontotients (A005277) that are the product of two totients (A002202).
[ "22", "22", "10", "46", "58", "46", "78", "82", "58", "46", "102", "22", "106", "82", "46", "138", "106", "82", "166", "172", "178", "190", "106", "226", "82", "166", "238", "172", "178", "22", "106", "262", "190", "282", "22", "106", "310", "316", "226", "82", "166", "238", "172", "346", "46", "178", "22", "358", "22", "10", "366", "106", "262", "382", "82", "388", "58", "22", "22", "46", "418" ]
[ "nonn" ]
11
1
1
[ "A002202", "A005277", "A329872", "A361058", "A361686" ]
null
Michel Marcus, Mar 29 2023
2023-03-29T12:12:04
oeisdata/seq/A361/A361686.seq
391cc3777954ef8c8e516ed542a323f0
A361687
The number of divisors of 2*n^2 which are <=n.
[ "1", "2", "3", "3", "3", "5", "3", "4", "5", "6", "3", "8", "3", "6", "8", "5", "3", "9", "3", "8", "9", "6", "3", "11", "5", "6", "7", "8", "3", "16", "3", "6", "9", "6", "8", "14", "3", "6", "9", "11", "3", "16", "3", "9", "13", "6", "3", "14", "5", "10", "9", "9", "3", "13", "9", "11", "9", "6", "3", "24", "3", "6", "14", "7", "9", "16", "3", "9", "9", "17", "3", "18", "3", "6", "14", "9", "8", "17", "3", "14", "9", "6", "3", "24", "9", "6", "9", "11" ]
[ "nonn" ]
13
1
2
[ "A361687", "A361689" ]
null
R. J. Mathar, Mar 20 2023
2023-03-21T12:31:34
oeisdata/seq/A361/A361687.seq
332e1216f1fb552f18932dcd031f79cd
A361688
a(n) = A361540(2*n,n) / binomial(2*n,n) for n >= 0.
[ "1", "2", "71", "10915", "4063645", "2842101221", "3255178907803", "5605980824208871", "13710496284516264953", "45746570903514799640905", "202291094041887013214628871", "1160411497892246920315488823067", "8496377826955803443098054623140629", "78398366060939693412478828210386035725" ]
[ "nonn" ]
6
0
2
[ "A000984", "A361540", "A361688" ]
null
Paul D. Hanna, Mar 20 2023
2023-03-24T09:03:54
oeisdata/seq/A361/A361688.seq
5f54455891c9812ad3f0a67655861e4a
A361689
The number of divisors of 2*n^2.
[ "2", "4", "6", "6", "6", "12", "6", "8", "10", "12", "6", "18", "6", "12", "18", "10", "6", "20", "6", "18", "18", "12", "6", "24", "10", "12", "14", "18", "6", "36", "6", "12", "18", "12", "18", "30", "6", "12", "18", "24", "6", "36", "6", "18", "30", "12", "6", "30", "10", "20", "18", "18", "6", "28", "18", "24", "18", "12", "6", "54", "6", "12", "30", "14", "18", "36", "6", "18", "18", "36", "6", "40", "6", "12", "30", "18", "18", "36", "6", "30" ]
[ "nonn", "easy" ]
13
1
1
[ "A000005", "A007814", "A048691", "A078644", "A275367", "A361689" ]
null
R. J. Mathar, Mar 20 2023
2023-03-21T12:31:15
oeisdata/seq/A361/A361689.seq
f0a2b88dbe3ba36c720074d9f8c98d17
A361690
Number of primes in the interval [2^n, 2^n + n].
[ "0", "2", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "0", "0", "3", "4", "0", "3", "0", "2", "1", "1", "3", "0", "0", "1", "0", "2", "1", "5", "1", "1", "2", "1", "0", "1", "2", "2", "2", "2", "1", "1", "2", "3", "0", "1", "3", "1", "0", "0", "1", "2", "2", "0", "3", "0", "2", "0", "0", "1", "3", "0", "1", "3", "0", "1", "2", "3", "1", "2", "2", "1", "1", "2", "3", "2", "4", "2", "2", "1", "2", "4", "1", "3", "0", "3", "2", "1", "2", "0" ]
[ "nonn" ]
31
0
2
[ "A000720", "A036378", "A143537", "A361690" ]
null
Jean-Marc Rebert, Mar 20 2023
2023-03-27T11:48:43
oeisdata/seq/A361/A361690.seq
4af23a2b5354951229dc05f5343cd1e0
A361691
Number of divisors of 7*n-1 of form 7*k+1.
[ "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "2", "1", "1", "3", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "3", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "2", "3", "1", "1", "2", "1", "1", "2", "1", "3", "1", "1", "1", "3", "1", "1", "1", "2", "1", "3", "1", "1", "1", "1", "1", "3", "2", "1", "1", "2", "1", "3", "1", "2", "2", "1", "1", "2", "1", "2", "1", "2", "1", "2", "1", "1", "1" ]
[ "nonn" ]
119
1
7
[ "A279061", "A361691", "A363808", "A363854", "A363855", "A363856", "A363857", "A363858" ]
null
Seiichi Manyama, Jun 24 2023
2023-06-25T10:39:44
oeisdata/seq/A361/A361691.seq
4cef630d25a5c0862ff044f57ceaa61d
A361692
a(n) = 17*n - 1.
[ "16", "33", "50", "67", "84", "101", "118", "135", "152", "169", "186", "203", "220", "237", "254", "271", "288", "305", "322", "339", "356", "373", "390", "407", "424", "441", "458", "475", "492", "509", "526", "543", "560", "577", "594", "611", "628", "645", "662", "679", "696", "713", "730", "747", "764", "781", "798", "815", "832", "849", "866", "883", "900", "917", "934", "951", "968", "985", "1002", "1019" ]
[ "nonn", "easy" ]
21
1
1
[ "A008590", "A008599", "A017257", "A361692" ]
null
Leo Tavares, Mar 20 2023
2025-04-03T17:16:14
oeisdata/seq/A361/A361692.seq
eba699d94563540724feac738b5b5a47
A361693
Index of where prime(n) first appears as a divisor of any term in A351495.
[ "2", "3", "6", "12", "19", "21", "29", "31", "39", "47", "49", "58", "65", "67", "75", "85", "93", "95", "104", "111", "113", "123", "131", "139", "150", "157", "159", "167", "169", "177", "196", "203", "213", "215", "231", "233", "242", "251", "259", "269", "277", "279", "295", "297", "305", "307", "325", "343", "351", "353", "361", "369", "371", "387", "397", "407", "415", "417", "426", "433", "435", "453", "472", "479" ]
[ "nonn" ]
8
1
1
[ "A351495", "A361330", "A361332", "A361333", "A361693" ]
null
Scott R. Shannon and N. J. A. Sloane, Mar 20 2023
2023-03-25T13:09:08
oeisdata/seq/A361/A361693.seq
bff91112bbe10b189af6e231edeb2567
A361694
Decimal expansion of (2 - phi)/3, with phi being the golden ratio A001622.
[ "1", "2", "7", "3", "2", "2", "0", "0", "3", "7", "5", "0", "0", "3", "5", "0", "5", "0", "5", "9", "8", "4", "7", "1", "0", "5", "5", "2", "1", "1", "4", "5", "3", "9", "6", "0", "7", "5", "9", "8", "9", "6", "9", "4", "0", "0", "6", "4", "7", "4", "5", "7", "1", "2", "6", "2", "1", "5", "1", "7", "1", "2", "5", "7", "6", "4", "9", "1", "3", "1", "7", "9", "0", "6", "0", "3", "6", "5", "8", "5", "0", "0", "9", "7", "5", "9", "7", "5", "9", "8", "6", "0", "3", "5", "3", "6", "2", "8", "7", "5", "0", "5" ]
[ "nonn", "cons" ]
19
0
2
[ "A001622", "A361694" ]
null
Jeremy Tan, Mar 22 2023
2023-04-14T15:39:36
oeisdata/seq/A361/A361694.seq
52b46b13a15408bc65f9f7c7cf7449a5
A361695
Number of ways of writing n^2 as a sum of seven squares.
[ "1", "14", "574", "3542", "18494", "43414", "145222", "235998", "591934", "860846", "1779974", "2256422", "4678982", "5195750", "9675918", "10983742", "18942014", "19873966", "35294686", "34670454", "57349894", "59707494", "92513302", "90116222", "149759302", "135668414", "213025750", "209185718", "311753358", "287144326", "450333422" ]
[ "nonn" ]
30
0
2
[ "A008451", "A065461", "A302996", "A361695" ]
null
Alois P. Heinz, Mar 22 2023
2023-04-04T15:49:22
oeisdata/seq/A361/A361695.seq
b3f272eb59d13b997e747f724eaa65df
A361696
Semiprimes of the form k^2 + 5.
[ "6", "9", "14", "21", "69", "86", "201", "329", "446", "489", "581", "681", "734", "789", "905", "1094", "1769", "1941", "2606", "2921", "3254", "3369", "3849", "3974", "4101", "4629", "4766", "6729", "7061", "7401", "8105", "8654", "9609", "9806", "10409", "10821", "11669", "12326", "13929", "17429", "17961", "19049", "20741", "23109", "23721", "24341", "27561", "30281", "31334", "32405" ]
[ "nonn", "easy" ]
11
1
1
[ "A001358", "A117951", "A144255", "A242333", "A360739", "A360740", "A360741", "A361696" ]
null
Elmo R. Oliveira, Mar 20 2023
2023-05-13T18:32:18
oeisdata/seq/A361/A361696.seq
ee62e732dd28cfd901d4785edf0ca0f9
A361697
The least y-value of the lower left corner of an n X n box with x-value n such that no edge of the box overlaps with a previous box, given that the first box has its lower left corner at (1,1).
[ "1", "2", "3", "4", "2", "6", "3", "8", "4", "7", "9", "12", "1", "11", "3", "16", "2", "13", "4", "17", "5", "20", "6", "24", "8", "14", "1", "25", "7", "21", "3", "32", "10", "22", "9", "31", "2", "23", "11", "37", "4", "26", "12", "42", "13", "29", "5", "48", "16", "33", "6", "40", "17", "28", "8", "53", "14", "36", "1", "51", "15", "35", "3", "64", "7", "46", "18", "56", "10", "44", "9", "67" ]
[ "nonn" ]
28
1
2
[ "A029744", "A131117", "A289523", "A361697", "A361742" ]
null
Kishore Rajesh, Mar 20 2023
2023-05-07T06:42:19
oeisdata/seq/A361/A361697.seq
3b51ec4cae2c7e07918563b71e11a629
A361698
The number of unlabeled connected 4 regular multigraphs on n nodes with 4 external legs, loops allowed.
[ "1", "1", "2", "8", "37", "181", "1010", "6135", "40893", "295753", "2317683", "19568427", "177397551", "1719790643", "17767328745", "194954224643", "2265042428226", "27785727158182", "358952560098959", "4871697965709175", "69309502018430799", "1031550920679805502", "16030923441853969843", "259682356008358417321", "4377679648827121988375" ]
[ "nonn" ]
13
0
3
[ "A085549", "A129429", "A361135", "A361454", "A361698" ]
null
R. J. Mathar, Mar 21 2023
2023-03-22T12:51:23
oeisdata/seq/A361/A361698.seq
4a3c4781391bc527ccbc9ad113b5d774
A361699
Constant term in the expansion of (1 + x^3 + y^3 + 1/(x*y))^n.
[ "1", "1", "1", "1", "1", "21", "121", "421", "1121", "2521", "6301", "23101", "99001", "386101", "1301301", "3943941", "11779041", "38241841", "136988041", "504616441", "1793870941", "6061831441", "19923689941", "66139128441", "227052188441", "800641330721", "2831644750221", "9870443816221", "33869987735221" ]
[ "nonn", "easy" ]
16
0
6
[ "A344560", "A361657", "A361699", "A361700" ]
null
Seiichi Manyama, Mar 21 2023
2023-03-22T07:54:51
oeisdata/seq/A361/A361699.seq
e9f9a3f80b751a7b46f2c1a6d8929930
A361700
Constant term in the expansion of (1 + x^4 + y^4 + 1/(x*y))^n.
[ "1", "1", "1", "1", "1", "1", "31", "211", "841", "2521", "6301", "13861", "30691", "90091", "360361", "1501501", "5645641", "18749641", "56063281", "157520641", "445836901", "1368402421", "4638690211", "16511900791", "58059667051", "195211574251", "625463703151", "1942351017751", "6016826006101", "19113287111101" ]
[ "nonn", "easy" ]
15
0
7
[ "A344560", "A361657", "A361699", "A361700" ]
null
Seiichi Manyama, Mar 21 2023
2023-03-22T07:18:53
oeisdata/seq/A361/A361700.seq
1997f6e5ecf366296c72233e26691a1d