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1999-12-11 03:00:00
2025-04-28 00:58:08
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A378001
a(n) is the (n-1)-th positive integer that is digitally balanced in base n.
[ "2", "15", "99", "722", "8410", "123813", "2177847", "44317852", "1023457869", "26432595075", "754777789018", "23609224082310", "802772380561983", "29480883458980947", "1162849439785414095", "49030176097150565512", "2200618769387073010719", "104753196945250864019109", "5271200265927977839358758" ]
[ "nonn", "base" ]
8
2
1
[ "A378000", "A378001" ]
null
Paolo Xausa, Nov 14 2024
2024-11-17T07:24:05
oeisdata/seq/A378/A378001.seq
71d9ba791829d72077422406dffb44da
A378002
Achilles numbers that are products of primorials.
[ "72", "288", "432", "864", "1152", "1800", "2592", "3456", "4608", "5400", "6912", "7200", "10368", "10800", "15552", "18432", "21600", "27648", "28800", "31104", "41472", "43200", "54000", "55296", "62208", "64800", "73728", "86400", "88200", "93312", "108000", "115200", "124416", "162000", "165888", "172800", "194400", "221184", "259200" ]
[ "nonn", "easy" ]
26
1
1
[ "A001597", "A001694", "A002110", "A007947", "A025487", "A052486", "A286708", "A364930", "A377854", "A378002" ]
null
Michael De Vlieger, Nov 16 2024
2024-11-17T07:10:10
oeisdata/seq/A378/A378002.seq
7ee8fab64c3c21b8e686a6265c43fd95
A378003
Decimal expansion of Pi*G - 7*zeta(3)/4, where G = A006752.
[ "7", "7", "3", "9", "9", "1", "2", "0", "1", "0", "7", "8", "8", "7", "1", "1", "5", "2", "3", "2", "8", "0", "3", "8", "3", "8", "3", "8", "7", "6", "5", "1", "0", "3", "1", "6", "2", "7", "6", "1", "2", "8", "3", "8", "8", "4", "5", "6", "8", "0", "6", "0", "3", "2", "6", "2", "5", "7", "2", "0", "5", "8", "0", "3", "0", "6", "6", "4", "4", "5", "7", "9", "2", "6", "5", "7", "4", "3", "0", "3", "4", "6", "7", "7", "5", "5", "8", "5", "3", "6", "4", "1", "4", "6", "9", "0", "6", "2", "9", "2" ]
[ "nonn", "cons" ]
16
0
1
[ "A000796", "A002117", "A006752", "A378003", "A378021" ]
null
Stefano Spezia, Nov 14 2024
2025-02-12T21:42:02
oeisdata/seq/A378/A378003.seq
dbc39c4be8c0dc49cf64e7909f2494d3
A378004
Number of winning positions of Gordon Hamilton's Jumping Frogs game with n single frogs, up to left-right symmetry.
[ "1", "1", "2", "5", "12", "39", "123", "412", "1431", "4831", "17363", "60697", "219777", "781260", "2858031", "10329091", "38103069", "138996792" ]
[ "nonn", "more" ]
24
1
3
[ "A000120", "A000217", "A030101", "A377232", "A377307", "A378004" ]
null
Glen Whitney, Nov 13 2024
2024-11-26T08:19:15
oeisdata/seq/A378/A378004.seq
11a269948f028687b655994e61241f86
A378005
Number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) such that p(i)-i is in {-2,4,5} for all i=1,...,n.
[ "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "3", "1", "0", "0", "0", "1", "6", "6", "1", "0", "0", "1", "10", "20", "10", "1", "1", "1", "15", "50", "50", "15", "6", "7", "21", "105", "175", "105", "36", "42", "49", "196", "490", "490", "231", "183", "217", "392", "1176", "1764", "1246", "785", "946", "1141", "2646", "5292", "5418", "3613", "3664", "4390", "6601", "14112", "19614" ]
[ "easy", "nonn" ]
8
0
14
[ "A001263", "A376743", "A377715", "A378005" ]
null
Michael A. Allen, Nov 13 2024
2024-12-03T12:40:28
oeisdata/seq/A378/A378005.seq
b37aa88c7c6ce1a367d86a61804249f8
A378006
Square table read by descending antidiagonals: the k-th column has Dirichlet g.f. Product_{chi} L(chi,s), where chi runs through all Dirichlet characters modulo k.
[ "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "1", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "2", "0", "1", "1", "1", "0", "0", "0", "0", "0", "2", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "2", "0", "1", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn", "tabl", "easy" ]
15
1
33
[ "A000012", "A000035", "A008442", "A045833", "A378006", "A378007" ]
null
Jianing Song, Nov 14 2024
2024-11-14T23:23:53
oeisdata/seq/A378/A378006.seq
766126d017c9cce80b491a7ba8de8a85
A378007
Square table read by descending antidiagonals: T(n,k) = A378006(k*n+1,k).
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "0", "1", "0", "1", "1", "1", "2", "4", "2", "2", "1", "1", "1", "2", "2", "1", "2", "1", "1", "1", "1", "2", "0", "2", "0", "0", "2", "1", "1", "1", "0", "4", "0", "1", "0", "3", "0", "1", "1", "1", "4", "6", "2", "6", "2", "4", "2", "1", "1", "1", "1", "0", "0", "0", "0", "0", "2", "0", "0", "2", "1", "1", "1", "4", "10", "4", "6", "4", "6", "2", "4", "2", "2", "1", "1" ]
[ "nonn", "tabl", "easy" ]
16
0
12
[ "A000012", "A008441", "A033687", "A097195", "A378006", "A378007", "A378008", "A378009", "A378010", "A378011", "A378012" ]
null
Jianing Song, Nov 14 2024
2024-11-14T23:23:28
oeisdata/seq/A378/A378007.seq
29900df2638f3efa8fd5ed152071667a
A378008
a(n) = b(5*n+1), with the sequence {b(n)} having Dirichlet g.f. Product_{chi} L(chi,s), where chi runs through all Dirichlet characters modulo 5; 5th column of A378007.
[ "1", "0", "4", "1", "0", "0", "4", "0", "4", "0", "0", "0", "4", "0", "4", "0", "1", "0", "0", "0", "4", "0", "0", "0", "10", "0", "4", "0", "0", "0", "4", "0", "0", "0", "0", "4", "4", "0", "4", "0", "0", "0", "4", "0", "0", "0", "0", "0", "4", "0", "4", "1", "0", "0", "4", "0", "4", "0", "0", "0", "0", "0", "4", "0", "0", "0", "4", "0", "16", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "4", "0", "0", "0", "4", "0", "4", "0", "0", "0", "16" ]
[ "nonn", "easy" ]
12
0
3
[ "A378007", "A378008" ]
null
Jianing Song, Nov 14 2024
2024-11-14T23:23:23
oeisdata/seq/A378/A378008.seq
ff28742095e2d5a486e7bfa3a3b7749f
A378009
a(n) = b(7*n+1), with the sequence {b(n)} having Dirichlet g.f. Product_{chi} L(chi,s), where chi runs through all Dirichlet characters modulo 7; 7th column of A378007.
[ "1", "2", "0", "0", "6", "0", "6", "0", "0", "3", "6", "0", "0", "0", "0", "0", "6", "0", "6", "0", "0", "0", "0", "0", "3", "0", "0", "0", "6", "0", "6", "0", "0", "12", "6", "0", "0", "0", "0", "0", "6", "0", "0", "0", "0", "0", "0", "0", "6", "12", "0", "0", "0", "0", "6", "0", "0", "0", "0", "0", "6", "0", "0", "0", "6", "0", "6", "0", "0", "0", "6", "0", "0", "4", "0", "0", "0", "0", "6", "0", "0", "12", "0", "0", "0", "0", "0", "0", "6", "0", "6" ]
[ "nonn", "easy" ]
12
0
2
[ "A378007", "A378009" ]
null
Jianing Song, Nov 14 2024
2024-11-14T23:23:19
oeisdata/seq/A378/A378009.seq
3b1890196864b97e5fdad0fd8e2ff102
A378010
a(n) = b(8*n+1), with the sequence {b(n)} having Dirichlet g.f. Product_{chi} L(chi,s), where chi runs through all Dirichlet characters modulo 8; 8th column of A378007.
[ "1", "2", "4", "2", "0", "4", "2", "0", "0", "4", "3", "4", "4", "0", "4", "2", "0", "4", "0", "8", "0", "2", "0", "0", "4", "0", "0", "0", "4", "4", "4", "0", "4", "0", "0", "4", "10", "0", "0", "4", "0", "0", "4", "0", "4", "2", "8", "0", "0", "0", "4", "4", "0", "8", "4", "4", "4", "4", "0", "0", "0", "0", "0", "0", "0", "4", "2", "0", "0", "0", "0", "4", "4", "0", "4", "4", "0", "4", "3", "0", "4", "0", "8", "0", "4", "0", "0", "16", "0", "0", "0" ]
[ "nonn", "easy" ]
12
0
2
[ "A378007", "A378010" ]
null
Jianing Song, Nov 14 2024
2024-11-14T23:23:14
oeisdata/seq/A378/A378010.seq
0e4cab45293e0f9953445d611741f028
A378011
a(n) = b(9*n+1), with the sequence {b(n)} having Dirichlet g.f. Product_{chi} L(chi,s), where chi runs through all Dirichlet characters modulo 9; 9th column of A378007.
[ "1", "0", "6", "0", "6", "0", "0", "1", "6", "0", "0", "0", "6", "0", "6", "0", "0", "0", "6", "0", "6", "0", "6", "0", "0", "0", "0", "0", "0", "0", "6", "0", "3", "0", "6", "0", "0", "0", "2", "0", "21", "0", "6", "0", "6", "0", "0", "0", "6", "0", "0", "0", "0", "0", "6", "0", "0", "0", "6", "0", "6", "0", "0", "0", "6", "0", "0", "0", "6", "0", "6", "0", "0", "0", "0", "0", "0", "0", "36", "0", "0", "0", "6", "0", "6", "0", "0", "0", "0", "0", "6" ]
[ "nonn", "easy" ]
12
0
3
[ "A378007", "A378011" ]
null
Jianing Song, Nov 14 2024
2024-11-14T23:23:10
oeisdata/seq/A378/A378011.seq
d2c18381483fc64a7978e2e5b007da0a
A378012
a(n) = b(10*n+1), with the sequence {b(n)} having Dirichlet g.f. Product_{chi} L(chi,s), where chi runs through all Dirichlet characters modulo 10; 10th column of A378007.
[ "1", "4", "0", "4", "4", "0", "4", "4", "1", "0", "4", "0", "10", "4", "0", "4", "0", "0", "4", "4", "0", "4", "0", "0", "4", "4", "0", "4", "4", "0", "0", "4", "0", "4", "16", "0", "2", "0", "0", "0", "4", "0", "4", "4", "0", "16", "4", "0", "0", "4", "0", "0", "4", "0", "4", "0", "0", "4", "0", "0", "4", "0", "0", "4", "4", "0", "4", "16", "0", "4", "4", "0", "0", "0", "0", "4", "4", "0", "16", "0", "0", "4", "4", "0", "2", "0", "0", "0", "4", "4", "0" ]
[ "nonn", "easy" ]
13
0
2
null
null
Jianing Song, Nov 14 2024
2024-11-14T20:13:53
oeisdata/seq/A378/A378012.seq
37fc5d12b97549828cd548671b3bbb85
A378013
Decimal expansion of A^2, where A is the lemniscate constant (A085565).
[ "1", "7", "1", "8", "7", "9", "6", "4", "5", "4", "5", "0", "5", "0", "9", "3", "2", "0", "6", "8", "7", "2", "5", "2", "3", "9", "4", "4", "9", "5", "2", "6", "3", "9", "2", "9", "9", "4", "7", "5", "2", "1", "4", "1", "1", "2", "9", "5", "4", "7", "9", "0", "2", "2", "4", "0", "6", "8", "6", "2", "1", "9", "7", "2", "8", "8", "4", "0", "0", "0", "8", "1", "9", "9", "0", "0", "2", "7", "8", "9", "1", "3", "1", "4", "5", "0", "7", "9", "1", "8", "9", "4", "0", "5", "3", "2", "5", "6", "9", "2" ]
[ "nonn", "cons" ]
15
1
2
[ "A085565", "A378013" ]
null
Vincenzo Librandi, Nov 14 2024
2025-02-05T00:16:04
oeisdata/seq/A378/A378013.seq
7c0d4457cf24fcf3a967678fb039f932
A378014
Triangle read by rows: T(n,k) = number of free hexagonal polyominoes with n cells, where the maximum number of cells on any lattice line is k. The term "lattice line" here means a line running through the cell centers and midpoints of their sides.
[ "1", "0", "1", "0", "2", "1", "0", "4", "2", "1", "0", "3", "15", "3", "1", "0", "5", "50", "23", "3", "1", "0", "1", "171", "126", "30", "4", "1", "0", "1", "506", "710", "187", "39", "4", "1", "0", "1", "1459", "3520", "1268", "270", "48", "5", "1", "0", "1", "3792", "16617", "7703", "1948", "364", "59", "5", "1", "0", "1", "9292", "72870", "45099", "12885", "2840", "488", "70", "6", "1" ]
[ "nonn", "tabl" ]
20
1
5
[ "A000228", "A377941", "A378014", "A378015" ]
null
Dave Budd, Nov 14 2024
2024-11-16T13:39:51
oeisdata/seq/A378/A378014.seq
fb02112f61befbc2fa89cfeb7e5dcf39
A378015
Triangle read by rows: T(n,k) = number of free hexagonal polyominoes with n cells, where the maximum number of collinear cell centers on any line in the plane is k.
[ "1", "0", "1", "0", "2", "1", "0", "4", "2", "1", "0", "2", "16", "3", "1", "0", "3", "52", "23", "3", "1", "0", "0", "169", "129", "30", "4", "1", "0", "0", "477", "740", "187", "39", "4", "1", "0", "0", "1245", "3729", "1274", "270", "48", "5", "1", "0", "0", "2750", "17578", "7785", "1948", "364", "59", "5", "1", "0", "0", "5380", "75827", "46045", "12895", "2840", "488", "70", "6", "1" ]
[ "nonn", "tabl" ]
9
1
5
[ "A000228", "A377756", "A377942", "A378014", "A378015" ]
null
Dave Budd, Nov 14 2024
2024-11-16T13:39:45
oeisdata/seq/A378/A378015.seq
ca037565038436b96a75adccc7a622fe
A378016
E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x)^2 * A(x) ).
[ "1", "2", "11", "115", "1617", "30241", "701923", "19517975", "633387905", "23513238865", "983268873891", "45750603668815", "2344878934878769", "131285573039583977", "7973124098907905603", "522086636316439329511", "36669284618683152764289", "2750044026126526125774625", "219342360538110975815216323" ]
[ "nonn" ]
8
0
2
[ "A376145", "A377828", "A377964", "A378016", "A378017" ]
null
Seiichi Manyama, Nov 14 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378016.seq
3acce2aae68b24c995c55116c1efe70b
A378017
E.g.f. satisfies A(x) = (1+x)^2 * exp( x * (1+x) * A(x) ).
[ "1", "3", "15", "148", "2077", "38326", "883369", "24431436", "789531705", "29213730010", "1218401262541", "56566561281616", "2893886178904549", "161768999193007974", "9811122121462081281", "641683497800057913556", "45022670799746182036465", "3373421864644139722767538", "268843153008388446079159573" ]
[ "nonn" ]
9
0
2
[ "A376145", "A377828", "A377966", "A378016", "A378017" ]
null
Seiichi Manyama, Nov 14 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378017.seq
bc79f0032dafa3a0e48d91e292c36e5a
A378018
Primes p which can be written as p = (A060735(k) +- next largest prime factor not in A060735(k)) for some k.
[ "3", "5", "7", "11", "13", "17", "19", "23", "29", "37", "53", "67", "83", "97", "113", "127", "157", "173", "199", "409", "431", "619", "641", "829", "1039", "1061", "1249", "1459", "1481", "1669", "1879", "1901", "2089", "2111", "2297", "6917", "9227", "13873", "16183", "18493", "23087", "25423", "27733", "30013", "30047", "60077", "90073" ]
[ "nonn" ]
17
1
1
[ "A000040", "A038708", "A060735", "A367182", "A378018" ]
null
Daniel D Gibson, Nov 14 2024
2024-12-23T13:50:21
oeisdata/seq/A378/A378018.seq
99509a37ce6dde6970113db1e746d0b3
A378019
E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x) ).
[ "1", "2", "9", "79", "957", "15441", "309943", "7468301", "210221385", "6774449185", "246049105131", "9947338595085", "443121311695021", "21568178966624993", "1138938283455953919", "64856665518838006861", "3961941908569940501649", "258453847468153873181889", "17932482767578645884498643" ]
[ "nonn" ]
10
0
2
[ "A362772", "A377827", "A377963", "A378019" ]
null
Seiichi Manyama, Nov 14 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378019.seq
9ccbecea42e3429558aa2ea355e26480
A378020
a(n) = pi(A020482(n)) - pi(A020481(n)).
[ "0", "0", "1", "2", "1", "3", "4", "3", "5", "6", "5", "7", "6", "5", "8", "9", "8", "7", "10", "9", "11", "12", "11", "13", "12", "11", "14", "13", "12", "15", "16", "15", "14", "17", "16", "18", "19", "18", "17", "20", "19", "21", "20", "19", "22", "21", "20", "14", "23", "22", "24", "25", "24", "26", "27", "26", "28", "27", "26", "23", "25", "24", "21", "29", "28", "30", "29", "28", "31", "32", "31", "30", "28", "29", "33", "34" ]
[ "nonn" ]
22
1
4
[ "A000720", "A020481", "A020482", "A377758", "A377972", "A378020" ]
null
Michel Eduardo Beleza Yamagishi, Nov 14 2024
2024-11-19T02:24:40
oeisdata/seq/A378/A378020.seq
1c1eaf5013ecc4d16c3f8c1b88b1b864
A378021
Decimal expansion of Pi*G - 33*zeta(3)/16, where G = A006752.
[ "3", "9", "8", "3", "4", "8", "4", "1", "8", "8", "4", "1", "4", "9", "7", "9", "3", "8", "1", "4", "0", "6", "2", "0", "2", "0", "8", "4", "0", "4", "1", "8", "2", "1", "9", "4", "1", "6", "2", "0", "7", "0", "1", "7", "2", "1", "0", "0", "4", "0", "0", "1", "3", "2", "0", "6", "5", "6", "3", "5", "7", "1", "9", "2", "6", "2", "3", "2", "0", "1", "3", "9", "9", "5", "7", "5", "2", "0", "1", "9", "3", "9", "9", "4", "2", "9", "1", "0", "7", "5", "9", "1", "1", "7", "7", "3", "3", "6", "1", "1" ]
[ "nonn", "cons" ]
6
0
1
[ "A000796", "A002117", "A006752", "A378003", "A378021" ]
null
Stefano Spezia, Nov 14 2024
2024-11-15T05:07:00
oeisdata/seq/A378/A378021.seq
21a98118218729c6e0cd7836c14defce
A378022
Let operator D(n) be the number formed by concatenation of the products of the decimal digits of n by their respective multiplicities. This sequence records the smallest number requiring n iterations of D to reach a stationary number; see Comment and Example.
[ "1", "11", "112", "166", "688", "4468", "22468", "112468", "124699", "1678999", "111367788889", "11112222333445666777778899" ]
[ "nonn", "base", "more" ]
19
0
2
[ "A351868", "A377948", "A378022" ]
null
David James Sycamore, Nov 14 2024
2024-11-19T14:22:05
oeisdata/seq/A378/A378022.seq
9c9bbbda195886555952f9e92f49930c
A378023
a(n) = (2*n^3 - 6*n^2 + 19*n - 9)*n/6.
[ "1", "7", "24", "66", "155", "321", "602", "1044", "1701", "2635", "3916", "5622", "7839", "10661", "14190", "18536", "23817", "30159", "37696", "46570", "56931", "68937", "82754", "98556", "116525", "136851", "159732", "185374", "213991", "245805", "281046", "319952", "362769", "409751", "461160", "517266", "578347", "644689" ]
[ "nonn", "easy" ]
10
1
2
null
null
Eric W. Weisstein, Nov 14 2024
2024-11-15T09:04:40
oeisdata/seq/A378/A378023.seq
299348e1209bf62833aa796964151733
A378024
Smallest k >= 10 whose decimal representation read in base (n+10) is a multiple of k.
[ "1913268348854", "11788", "1557", "126357", "145", "1038", "1757", "116", "153", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "10", "21", "11", "23", "12", "25", "13", "27", "14", "29", "10", "31", "16", "11", "17", "35", "12", "37", "19", "13", "10", "41", "14", "43", "11", "15", "23", "47", "12", "49", "10", "17", "13", "53", "18", "11", "14", "19", "29", "59", "10", "61" ]
[ "base", "nonn" ]
20
1
1
[ "A139285", "A378024" ]
null
Sergio Pimentel, Nov 14 2024
2024-12-01T11:40:04
oeisdata/seq/A378/A378024.seq
4f621c6fd6085c96969d61c591f97a1b
A378025
Decimal expansion of 1/2 - log(2)/4 - G/Pi, where G = A006752.
[ "0", "3", "5", "1", "5", "2", "3", "0", "0", "8", "2", "9", "1", "9", "4", "8", "9", "2", "5", "0", "7", "3", "0", "7", "5", "1", "3", "1", "6", "7", "0", "6", "0", "9", "3", "9", "1", "1", "7", "0", "5", "8", "8", "1", "2", "4", "2", "4", "0", "9", "8", "9", "1", "6", "2", "0", "8", "8", "2", "8", "4", "2", "8", "5", "1", "4", "9", "0", "3", "9", "5", "7", "6", "2", "7", "1", "3", "7", "4", "5", "9", "3", "7", "1", "9", "0", "7", "3", "4", "3", "9", "4", "7", "7", "6", "1", "2", "6", "9", "2", "0" ]
[ "nonn", "cons" ]
10
0
2
[ "A000796", "A002162", "A006752", "A143233", "A378025" ]
null
Stefano Spezia, Nov 14 2024
2025-04-02T11:00:38
oeisdata/seq/A378/A378025.seq
feb551dc267617c5ecbcb8e229f36ab2
A378026
Number of simple lattice paths, steps (-1,0,0),(0,-1,0),(0,0,-1), of length 3n from (n,n,n) to the origin, never returning to the diagonal x = y = z before the origin.
[ "1", "6", "54", "816", "14814", "295812", "6262488", "137929392", "3125822238", "72383434332", "1704669773652", "40693683620448", "982302086191752", "23933136140685648", "587728374471479952", "14530886841268923264", "361374588105759096606", "9033515437023805672044", "226844689948433272890396", "5719461854507320708714464" ]
[ "nonn", "walk" ]
27
0
2
[ "A000984", "A006480", "A054474", "A378026" ]
null
Markus Kuba, Nov 14 2024
2025-04-04T15:02:28
oeisdata/seq/A378/A378026.seq
7b8210d001121ac4ea731320070ba84c
A378027
a(n) = prime(prime(prime(n))) - prime(prime(n)).
[ "2", "6", "20", "42", "96", "138", "218", "264", "348", "490", "582", "762", "884", "962", "1086", "1282", "1510", "1564", "1890", "2028", "2110", "2348", "2570", "2798", "3128", "3396", "3528", "3686", "3798", "3932", "4672", "4884", "5096", "5316", "5802", "5946", "6274", "6640", "6850", "7190", "7464", "7632", "8166", "8290", "8538", "8642", "9334", "10334", "10520", "10650", "10830", "11048", "11240", "11872", "12088", "12508" ]
[ "nonn", "easy" ]
42
1
1
[ "A000040", "A006450", "A014689", "A038580", "A168152", "A378027" ]
null
Sean M. Drury, Nov 17 2024
2024-11-25T09:08:43
oeisdata/seq/A378/A378027.seq
942ffd84f38ffed2f81a8b5b0fa6cff3
A378028
Positions of records in A377059.
[ "1", "4", "9", "17", "22", "25", "46", "49", "81", "118", "121", "169", "243", "334", "337", "343", "361", "529", "841", "961", "1331", "1369", "2187", "2197", "2209", "2809", "3481", "3721", "4489", "5041", "6241", "6859", "6889", "7921", "10201", "11449", "12167", "14641", "16129", "17161", "19321", "22201", "24389", "26569", "27889", "29791", "29929", "32041", "32761", "38809", "39601", "44521", "49729" ]
[ "nonn" ]
9
1
2
[ "A000010", "A001122", "A001220", "A244623", "A377059", "A378028", "A378029" ]
null
Robert Israel, Nov 14 2024
2024-11-17T07:29:56
oeisdata/seq/A378/A378028.seq
7e0d96b5a8133ccb36f2ecdbee8e2e26
A378029
Record values in A377059.
[ "0", "2", "6", "8", "10", "20", "22", "42", "54", "58", "110", "156", "162", "166", "168", "294", "342", "506", "812", "930", "1210", "1332", "1458", "2028", "2162", "2756", "3422", "3660", "4422", "4970", "6162", "6498", "6806", "7832", "10100", "11342", "11638", "13310", "16002", "17030", "19182", "22052", "23548", "26406", "27722", "28830", "29756", "31862", "32580", "38612", "39402", "44310", "49506" ]
[ "nonn" ]
7
1
2
[ "A377059", "A378028", "A378029" ]
null
Robert Israel, Nov 14 2024
2024-11-17T07:30:07
oeisdata/seq/A378/A378029.seq
d30fa631b5641b3f277fe864dfa85daf
A378030
Lexicographically earliest sequence of distinct positive integers such that a(a(n)) = a(a(n)-1) + a(a(n)-2).
[ "3", "4", "7", "11", "6", "17", "23", "9", "32", "12", "44", "56", "14", "70", "16", "86", "102", "19", "121", "21", "142", "24", "166", "190", "26", "216", "28", "244", "30", "274", "33", "307", "340", "35", "375", "37", "412", "39", "451", "41", "492", "43", "535", "578", "46", "624", "48", "672", "50", "722", "52", "774", "54", "828", "57", "885", "942", "59", "1001", "61", "1062", "63", "1125", "65", "1190", "67", "1257", "69", "1326", "1395", "72", "1467", "74", "1541", "76", "1617", "78", "1695", "80" ]
[ "nonn" ]
12
1
1
[ "A000045", "A004001", "A005185", "A007378", "A105753", "A121053", "A378030" ]
null
Scott R. Shannon, Nov 14 2024
2024-11-15T23:39:16
oeisdata/seq/A378/A378030.seq
ecdcbdfa2c3f7137917bd3a9c853011f
A378031
Cogrowth sequence for the 18-element group C6 X C3 = <S,T | S^6, T^3, [S,T]>.
[ "1", "1", "2", "85", "926", "5461", "37130", "349525", "2973350", "22369621", "174174002", "1431655765", "11582386286", "91625968981", "729520967450", "5864062014805", "47006639297270", "375299968947541", "2999857885752002", "24019198012642645", "192222214478506046", "1537228672809129301" ]
[ "nonn", "easy" ]
6
0
3
[ "A007613", "A095364", "A377627", "A378031", "A378109", "A378110", "C2", "C3", "C6", "D9", "S3" ]
null
Sean A. Irvine, Nov 14 2024
2024-11-16T16:24:34
oeisdata/seq/A378/A378031.seq
d5e943a83f23f23c8c52d5d4be7de8d0
A378032
a(1) = a(2) = 1; a(n>2) is the greatest nonsquarefree number < prime(n).
[ "1", "1", "4", "4", "9", "12", "16", "18", "20", "28", "28", "36", "40", "40", "45", "52", "56", "60", "64", "68", "72", "76", "81", "88", "96", "100", "100", "104", "108", "112", "126", "128", "136", "136", "148", "150", "156", "162", "164", "172", "176", "180", "189", "192", "196", "198", "208", "220", "225", "228", "232", "236", "240", "250", "256", "261", "268", "270" ]
[ "nonn" ]
7
1
3
[ "A000040", "A001223", "A005117", "A013929", "A036263", "A053797", "A053806", "A061351", "A061398", "A061399", "A065514", "A065890", "A068360", "A068361", "A070321", "A072284", "A078147", "A112925", "A112926", "A120327", "A224363", "A337030", "A345531", "A366833", "A376593", "A377046", "A377047", "A377048", "A377049", "A377050", "A377430", "A377431", "A377703", "A377781", "A377783", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378082", "A378083", "A378084", "A378086" ]
null
Gus Wiseman, Nov 16 2024
2024-11-17T21:39:02
oeisdata/seq/A378/A378032.seq
5d5aa84accf6978024500ca3a6dac68f
A378033
Greatest nonsquarefree number <= n, or 1 if there is none (the case n <= 3).
[ "1", "1", "1", "4", "4", "4", "4", "8", "9", "9", "9", "12", "12", "12", "12", "16", "16", "18", "18", "20", "20", "20", "20", "24", "25", "25", "27", "28", "28", "28", "28", "32", "32", "32", "32", "36", "36", "36", "36", "40", "40", "40", "40", "44", "45", "45", "45", "48", "49", "50", "50", "52", "52", "54", "54", "56", "56", "56", "56", "60", "60", "60", "63", "64", "64", "64", "64", "68" ]
[ "nonn" ]
6
1
4
[ "A000040", "A001223", "A005117", "A013929", "A031218", "A036263", "A053797", "A053806", "A057627", "A061398", "A061399", "A067535", "A068360", "A068361", "A070321", "A076259", "A078147", "A112925", "A112926", "A120327", "A162966", "A337030", "A376590", "A376593", "A377046", "A377047", "A377048", "A377049", "A377050", "A377782", "A377783", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378082", "A378083", "A378084", "A378085", "A378086", "A378087" ]
null
Gus Wiseman, Nov 18 2024
2024-11-19T17:25:01
oeisdata/seq/A378/A378033.seq
f469ddd2d04b98ad7cbf9adeea1dea53
A378034
First-differences of A378032 (greatest number < prime(n) that is 1 or nonsquarefree).
[ "0", "3", "0", "5", "3", "4", "2", "2", "8", "0", "8", "4", "0", "5", "7", "4", "4", "4", "4", "4", "4", "5", "7", "8", "4", "0", "4", "4", "4", "14", "2", "8", "0", "12", "2", "6", "6", "2", "8", "4", "4", "9", "3", "4", "2", "10", "12", "5", "3", "4", "4", "4", "10", "6", "5", "7", "2", "6", "4", "0", "12", "14", "2", "4", "4", "12", "8", "8", "4", "4", "4", "8", "8", "6", "2", "8", "8", "4", "8", "8", "4", "8", "4", "4" ]
[ "nonn" ]
5
1
2
[ "A000040", "A001223", "A005117", "A013929", "A036263", "A053797", "A053806", "A061398", "A061399", "A065514", "A065890", "A068360", "A068361", "A070321", "A072284", "A078147", "A112925", "A112926", "A120327", "A162966", "A224363", "A337030", "A345531", "A376593", "A377046", "A377047", "A377048", "A377049", "A377050", "A377430", "A377431", "A377703", "A377781", "A377783", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378082", "A378083", "A378084", "A378086" ]
null
Gus Wiseman, Nov 18 2024
2024-11-19T22:12:20
oeisdata/seq/A378/A378034.seq
7e21c943ef8fbde9e0b0fe26e0d5f581
A378035
Greatest perfect power < prime(n).
[ "1", "1", "4", "4", "9", "9", "16", "16", "16", "27", "27", "36", "36", "36", "36", "49", "49", "49", "64", "64", "64", "64", "81", "81", "81", "100", "100", "100", "100", "100", "125", "128", "128", "128", "144", "144", "144", "144", "144", "169", "169", "169", "169", "169", "196", "196", "196", "216", "225", "225", "225", "225", "225", "243", "256", "256", "256", "256" ]
[ "nonn" ]
22
1
3
[ "A000015", "A000040", "A000961", "A001223", "A001597", "A007916", "A007918", "A031218", "A045542", "A052410", "A053289", "A057820", "A065514", "A067871", "A069623", "A076411", "A076412", "A080769", "A081676", "A131605", "A188951", "A216765", "A345531", "A375706", "A377283", "A377432", "A377434", "A377436", "A377466", "A377468", "A378032", "A378035", "A378249", "A378250", "A378251", "A378253", "A378355", "A378356" ]
null
Gus Wiseman, Nov 23 2024
2024-11-26T02:18:37
oeisdata/seq/A378/A378035.seq
d060f87520ffe8444529c6512beae95e
A378036
First differences of A378033 (greatest positive integer < n that is 1 or nonsquarefree).
[ "0", "0", "3", "0", "0", "0", "4", "1", "0", "0", "3", "0", "0", "0", "4", "0", "2", "0", "2", "0", "0", "0", "4", "1", "0", "2", "1", "0", "0", "0", "4", "0", "0", "0", "4", "0", "0", "0", "4", "0", "0", "0", "4", "1", "0", "0", "3", "1", "1", "0", "2", "0", "2", "0", "2", "0", "0", "0", "4", "0", "0", "3", "1", "0", "0", "0", "4", "0", "0", "0", "4", "0", "0", "3", "1", "0", "0", "0", "4", "1", "0", "0", "3", "0", "0", "0", "4", "0", "2", "0", "2", "0", "0", "0", "4", "0", "2", "1", "1", "0", "0", "0", "4", "0", "0", "0", "4" ]
[ "nonn" ]
11
1
3
[ "A000040", "A001223", "A005117", "A013929", "A036263", "A053797", "A053806", "A061398", "A061399", "A065514", "A067535", "A068360", "A068361", "A070321", "A076259", "A078147", "A112925", "A112926", "A120327", "A162966", "A337030", "A376590", "A376593", "A377046", "A377047", "A377048", "A377049", "A377050", "A377703", "A377783", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378082", "A378083", "A378084", "A378085", "A378086", "A378087" ]
null
Gus Wiseman, Nov 18 2024
2025-01-28T20:51:46
oeisdata/seq/A378/A378036.seq
efd07ff8a3fb5c26244805cd301fbde5
A378037
First differences of A112926 (smallest squarefree integer > prime(n)).
[ "2", "1", "4", "3", "1", "5", "2", "5", "4", "3", "5", "4", "4", "5", "4", "6", "1", "7", "4", "1", "8", "3", "6", "10", "1", "3", "4", "1", "4", "15", "4", "5", "3", "10", "3", "4", "7", "5", "4", "7", "1", "11", "1", "5", "2", "12", "13", "3", "1", "5", "6", "5", "7", "5", "7", "6", "2", "5", "4", "3", "10", "14", "4", "1", "4", "16", "5", "10", "4", "1", "8", "8", "4", "7", "4", "5", "8", "4", "8", "11", "1", "11", "1" ]
[ "nonn" ]
8
1
1
[ "A000040", "A001223", "A005117", "A007674", "A013928", "A013929", "A036263", "A045882", "A053797", "A053806", "A061398", "A061399", "A067535", "A068360", "A068361", "A070321", "A072284", "A073247", "A078147", "A112925", "A112926", "A120327", "A280892", "A376593", "A377703", "A377783", "A377784", "A378032", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378084", "A378085", "A378087" ]
null
Gus Wiseman, Dec 04 2024
2024-12-04T15:44:10
oeisdata/seq/A378/A378037.seq
f47a02e07034e1a5b8450e3a4f0638ba
A378038
First differences of A112925 = greatest squarefree number < prime(n).
[ "1", "1", "3", "4", "1", "4", "2", "5", "4", "4", "5", "4", "3", "4", "5", "7", "1", "7", "4", "1", "7", "4", "5", "8", "2", "5", "4", "1", "4", "12", "7", "4", "4", "8", "3", "6", "6", "5", "4", "8", "1", "11", "1", "4", "2", "13", "12", "4", "1", "4", "7", "1", "10", "6", "7", "5", "2", "5", "4", "4", "9", "14", "5", "1", "3", "16", "5", "11", "1", "2", "9", "8", "5", "6", "5", "4", "9", "4", "8", "11", "1", "11", "1", "7" ]
[ "nonn" ]
4
1
3
[ "A000040", "A001223", "A005117", "A007674", "A013928", "A013929", "A036263", "A045882", "A053797", "A053806", "A061398", "A061399", "A067535", "A068360", "A068361", "A070321", "A072284", "A073247", "A078147", "A112925", "A112926", "A120327", "A280892", "A376593", "A377703", "A377781", "A377783", "A377784", "A378032", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378084", "A378085", "A378087" ]
null
Gus Wiseman, Dec 04 2024
2024-12-04T15:40:38
oeisdata/seq/A378/A378038.seq
6a6c6f904d59ff8f2ea1235315eae4a6
A378039
a(1)=3; a(n>1) = n-th first difference of A120327(k) = least nonsquarefree number greater than k.
[ "3", "0", "0", "4", "0", "0", "0", "1", "3", "0", "0", "4", "0", "0", "0", "2", "0", "2", "0", "4", "0", "0", "0", "1", "2", "0", "1", "4", "0", "0", "0", "4", "0", "0", "0", "4", "0", "0", "0", "4", "0", "0", "0", "1", "3", "0", "0", "1", "1", "2", "0", "2", "0", "2", "0", "4", "0", "0", "0", "3", "0", "0", "1", "4", "0", "0", "0", "4", "0", "0", "0", "3", "0", "0", "1", "4", "0", "0", "0", "1", "3", "0", "0", "4", "0", "0", "0" ]
[ "nonn" ]
6
1
1
[ "A000015", "A000040", "A001223", "A005117", "A007675", "A013928", "A013929", "A036263", "A053797", "A053806", "A061398", "A061399", "A068360", "A068361", "A068781", "A070321", "A072284", "A073247", "A073248", "A078147", "A112926", "A120327", "A224363", "A376593", "A377047", "A377049", "A377780", "A377782", "A377783", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378039", "A378040", "A378082", "A378083", "A378084", "A378085", "A378087" ]
null
Gus Wiseman, Nov 18 2024
2024-11-19T22:12:11
oeisdata/seq/A378/A378039.seq
fcc3c9a0ad2137172a48a09513ca4933
A378040
Union of A377783(n) = least nonsquarefree number > prime(n).
[ "4", "8", "12", "16", "18", "20", "24", "32", "40", "44", "48", "54", "60", "63", "68", "72", "75", "80", "84", "90", "98", "104", "108", "112", "116", "128", "132", "140", "150", "152", "160", "164", "168", "175", "180", "184", "192", "196", "198", "200", "212", "224", "228", "232", "234", "240", "242", "252", "260", "264", "270", "272", "279", "284", "294", "308", "312" ]
[ "nonn" ]
6
1
1
[ "A000015", "A000040", "A001223", "A005117", "A013928", "A013929", "A036263", "A053797", "A053806", "A057627", "A061398", "A061399", "A068360", "A068361", "A070321", "A071403", "A072284", "A078147", "A112925", "A112926", "A120327", "A224363", "A337030", "A345531", "A376593", "A377047", "A377049", "A377430", "A377431", "A377703", "A377783", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378082", "A378083", "A378084", "A378086" ]
null
Gus Wiseman, Nov 20 2024
2024-11-20T20:45:20
oeisdata/seq/A378/A378040.seq
1246e1f3890180a902d38d259b057952
A378041
E.g.f. satisfies A(x) = exp( x * A(x)^2 / (1-x) ) / (1-x).
[ "1", "2", "15", "220", "4873", "145446", "5479639", "249736936", "13366083889", "821950542730", "57117681241471", "4426656694204020", "378577567656396409", "35416929943920575662", "3598006167290727776263", "394460149364865110384896", "46420283015545052734709473", "5836509710708683465245181458" ]
[ "nonn" ]
10
0
2
[ "A377595", "A378041", "A378042" ]
null
Seiichi Manyama, Nov 15 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378041.seq
81cdcf6887facb64f8d950ac1b3f5199
A378042
E.g.f. satisfies A(x) = exp( x * A(x)^3 / (1-x) ) / (1-x).
[ "1", "2", "19", "385", "12041", "512101", "27616705", "1806241151", "138948411649", "12294333869545", "1230146587626041", "137347201671983227", "16928938651265737585", "2283232081600363345037", "334480117852142180147377", "52888942867094899879009111", "8978241760087200983202588545", "1628601738501672908949881316433" ]
[ "nonn" ]
8
0
2
[ "A377595", "A378041", "A378042" ]
null
Seiichi Manyama, Nov 15 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378042.seq
1f4701216b8c93c8210980b88153e88e
A378043
E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^2 ).
[ "1", "2", "13", "190", "4045", "116746", "4251289", "187255174", "9684799961", "575477786674", "38638577549701", "2893159369162030", "239045577899472997", "21604942464613062010", "2120362938300115706513", "224568728344893756230326", "25529660577970226603535793", "3100816199696659908092912866" ]
[ "nonn" ]
11
0
2
[ "A377894", "A378019", "A378043", "A378044", "A378045" ]
null
Seiichi Manyama, Nov 15 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378043.seq
46e4fac07f110f02ba91d293d5a9c5af
A378044
E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^3 ).
[ "1", "2", "17", "349", "10661", "444161", "23447635", "1500738989", "112954047113", "9777254959729", "956963374613471", "104510139881448797", "12599380858829314093", "1662018439019972570681", "238128379446158082330779", "36825779588890274967294061", "6113887910300601007096973585", "1084611999181162104894547358561" ]
[ "nonn" ]
11
0
2
[ "A377895", "A378019", "A378043", "A378044" ]
null
Seiichi Manyama, Nov 15 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378044.seq
8aaf5f286853982e7efe0ac81157fafb
A378045
E.g.f. satisfies A(x) = (1+x) * exp(x * A(x)^2 / (1+x)).
[ "1", "2", "9", "100", "1693", "39046", "1140589", "40379872", "1680490361", "80409242314", "4349556199441", "262478904794140", "17482853419143061", "1274026039224276430", "100830973069183104245", "8612770277501109271576", "789749958006001265241073", "77375794118912255978104978", "8066966112797470401673208089" ]
[ "nonn" ]
13
0
2
[ "A362773", "A377826", "A377894", "A378043", "A378045", "A378046" ]
null
Seiichi Manyama, Nov 15 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378045.seq
9efd392fdbc72e8f48127e5545bc6446
A378046
E.g.f. satisfies A(x) = (1+x) * exp(x * A(x)^3 / (1+x)^2).
[ "1", "2", "11", "169", "4049", "132881", "5542495", "280694135", "16730578625", "1147444968385", "89015365063991", "7707022678811567", "736734708409976017", "77070404075178587633", "8757816984586841345231", "1074244834335107678837191", "141469329806979182825146625", "19908315372027482035799282177" ]
[ "nonn" ]
10
0
2
[ "A363478", "A377826", "A378045", "A378046" ]
null
Seiichi Manyama, Nov 15 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378046.seq
cdafcdaea16261e7c9ec551062a2d83d
A378047
E.g.f. satisfies A(x) = (1+x)^2 * exp(x * A(x) / (1+x)).
[ "1", "3", "11", "70", "685", "8966", "147769", "2938608", "68509193", "1832813866", "55354862701", "1863179311676", "69163696768093", "2807246931378462", "123685264726805825", "5879149578658117096", "299892675674572370065", "16340561709320173229906", "947234845622653951286485" ]
[ "nonn" ]
15
0
2
[ "A362771", "A377826", "A378047" ]
null
Seiichi Manyama, Nov 15 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378047.seq
2401094b407c4b0d1162f408b7a75691
A378048
Numbers k such that k and k^2 together use at most 4 distinct decimal digits.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "19", "20", "21", "22", "23", "25", "26", "27", "28", "30", "31", "35", "38", "40", "41", "45", "46", "50", "55", "56", "60", "63", "64", "65", "66", "68", "70", "74", "75", "76", "77", "80", "81", "83", "85", "88", "90", "91", "95", "96", "97", "99", "100", "101", "102", "105", "109", "110" ]
[ "nonn", "base" ]
52
1
3
[ "A043537", "A053061", "A055436", "A136808", "A136809", "A136816", "A136822", "A154155", "A378048" ]
null
Jovan Radenkovicc, Nov 15 2024
2025-02-02T16:30:58
oeisdata/seq/A378/A378048.seq
d254ad18dc772b812dc4b2b8b51ef52d
A378049
Numbers k such that the least m for which m*k is a lucky number (if such an m exists) sets a new record.
[ "1", "5", "19", "59", "121", "1843", "6233", "57637", "84019", "183023" ]
[ "nonn", "more" ]
10
1
2
[ "A000959", "A377776", "A378049", "A378050", "A378051" ]
null
Pontus von Brömssen, Nov 15 2024
2024-11-15T11:15:44
oeisdata/seq/A378/A378049.seq
0a2264198913097248a9846edba554e6
A378050
Records in A377776.
[ "1", "3", "7", "15", "67", "69", "123", "145", "151", "221" ]
[ "nonn", "more" ]
5
1
2
[ "A000959", "A377776", "A378049", "A378050", "A378052" ]
null
Pontus von Brömssen, Nov 15 2024
2024-11-15T11:15:54
oeisdata/seq/A378/A378050.seq
b256ef27fb2400b789030b8a8a5c4ff3
A378051
Numbers k such that the least m for which m*k is a ludic number (if such an m exists) sets a new record.
[ "1", "19", "49", "59", "365", "695", "1055", "1171", "1655", "2945", "5767", "12085", "12715", "68585" ]
[ "nonn", "more" ]
6
1
2
[ "A003309", "A377778", "A378049", "A378051", "A378052" ]
null
Pontus von Brömssen, Nov 15 2024
2024-11-15T11:15:47
oeisdata/seq/A378/A378051.seq
0f0996faff202a42041186b728fd3695
A378052
Records in A377778.
[ "1", "11", "19", "31", "41", "47", "53", "59", "77", "89", "133", "247", "253", "347" ]
[ "nonn", "more" ]
5
1
2
[ "A003309", "A377778", "A378050", "A378051", "A378052" ]
null
Pontus von Brömssen, Nov 15 2024
2024-11-15T11:15:51
oeisdata/seq/A378/A378052.seq
e622b4d0702ae60b66f81c8cde39205a
A378053
a(n) = gcd(Product_{d|n} (d + 1), Product_{d|n, d>1} (d - 1)) = gcd(A020696(n), A377484(n)).
[ "1", "1", "2", "3", "4", "2", "2", "3", "16", "36", "2", "30", "4", "6", "16", "45", "4", "80", "2", "108", "16", "6", "2", "210", "24", "12", "32", "18", "4", "1008", "2", "45", "64", "12", "48", "8400", "4", "18", "16", "2268", "4", "240", "2", "90", "512", "18", "2", "3150", "32", "216", "64", "540", "4", "160", "144", "2430", "32", "12", "2", "166320", "4", "6", "1280", "405", "48", "1344" ]
[ "nonn" ]
10
1
3
[ "A000079", "A002144", "A002145", "A020696", "A377484", "A378053", "A378056" ]
null
Amiram Eldar, Nov 15 2024
2024-11-15T11:17:16
oeisdata/seq/A378/A378053.seq
8cf32d55eb92b2cfa241ead84845b5f9
A378054
Numbers k that divide A378053(k) = gcd(Product_{d|k} (d + 1), Product_{d|k, d>1} (d - 1)).
[ "1", "60", "90", "120", "144", "168", "180", "210", "240", "252", "280", "336", "360", "420", "504", "540", "560", "630", "660", "720", "840", "900", "924", "990", "1008", "1056", "1080", "1092", "1200", "1260", "1320", "1404", "1440", "1512", "1560", "1680", "1800", "1848", "1872", "1890", "1980", "2016", "2100", "2112", "2160", "2184", "2310", "2376", "2400" ]
[ "nonn" ]
8
1
2
[ "A020696", "A056954", "A355331", "A377484", "A378053", "A378054", "A378055", "A378058" ]
null
Amiram Eldar, Nov 15 2024
2024-11-15T11:17:29
oeisdata/seq/A378/A378054.seq
64e43d16756f777d8f365d8f4634225a
A378055
Numbers k such that k | A378053(k) and (k+1) | A378053(k+1).
[ "638000", "13466816", "14753024", "16092999", "19494189", "38137749", "63668079", "80061344", "86119704", "107232255", "112375899", "121550624", "127205000", "154466675", "294147854", "391738599", "553140224", "561712095", "682199595", "728999999", "871651143", "879207615", "911062844", "920985624", "1017609999" ]
[ "nonn" ]
6
1
1
[ "A020696", "A355332", "A377484", "A377949", "A378053", "A378054", "A378055", "A378059" ]
null
Amiram Eldar, Nov 15 2024
2024-11-15T13:10:45
oeisdata/seq/A378/A378055.seq
cb7aad4c2c9eaca8021ebaa1287e5601
A378056
a(n) = gcd(A057643(n), A084190(n)) = gcd(lcm{d+1 : d|n}, lcm{d-1 : d > 1 and d|n}).
[ "1", "1", "2", "3", "2", "2", "2", "3", "4", "6", "2", "30", "2", "6", "4", "15", "2", "20", "2", "6", "4", "6", "2", "210", "6", "6", "4", "6", "2", "84", "2", "15", "4", "6", "12", "420", "2", "6", "4", "126", "2", "60", "2", "30", "8", "6", "2", "210", "8", "6", "4", "30", "2", "20", "12", "90", "4", "6", "2", "4620", "2", "6", "40", "45", "6", "84", "2", "6", "4", "36", "2", "420", "2", "6", "24", "30", "12" ]
[ "nonn" ]
10
1
3
[ "A000079", "A057643", "A084190", "A378053", "A378056", "A378057" ]
null
Amiram Eldar, Nov 15 2024
2024-11-16T02:56:26
oeisdata/seq/A378/A378056.seq
591129a61ba339962630af5ec488f67a
A378057
Composite numbers k such that A378056(k) = gcd(lcm{d+1 : d|k}, lcm{d-1 : d > 1 and d|k}) = 2.
[ "6", "481", "793", "949", "1417", "2041", "2257", "2509", "2701", "2977", "3133", "3589", "3601", "4033", "4069", "4453", "4849", "5161", "5317", "5809", "5917", "5941", "6697", "7033", "7081", "7141", "7501", "7957", "7969", "8593", "8917", "9217", "9529", "9577", "10249", "10573", "10777", "11041", "11401", "11461", "11581", "11773", "12469", "12913", "12961" ]
[ "nonn" ]
7
1
1
[ "A378056", "A378057" ]
null
Amiram Eldar, Nov 15 2024
2024-11-15T12:56:40
oeisdata/seq/A378/A378057.seq
ea01b8505a03becdd7f8b3d58d34df8e
A378058
Numbers k that divide A378056(k) = gcd(lcm{d+1 : d|k}, lcm{d-1 : d > 1 and d|k}).
[ "1", "60", "210", "360", "420", "504", "630", "660", "840", "924", "1092", "1260", "1320", "1560", "1848", "1980", "2184", "2310", "2520", "2640", "2772", "3080", "3120", "3276", "3465", "3960", "4080", "4284", "4620", "4680", "5320", "5460", "5544", "6006", "6552", "6732", "6840", "6864", "6930", "7140", "7800", "7854", "7920", "8190", "8280", "8568", "8580", "9240", "9360", "9828" ]
[ "nonn" ]
11
1
2
[ "A377950", "A377952", "A378054", "A378056", "A378058", "A378059" ]
null
Amiram Eldar, Nov 15 2024
2024-11-15T12:56:18
oeisdata/seq/A378/A378058.seq
8808db65dac91fa52aec4de4d828f9e2
A378059
Numbers k such k | A378056(k) and (k+1) | A378056(k+1).
[ "112375899", "871651143", "1525038515", "3524721824", "6058144224", "7616307699", "7929320399", "9778346864", "10799650575", "11536526000", "13663711775", "20596306224", "22326106256", "24442111385", "26385908912", "27394105760", "28476579725", "31552570400", "34148839725", "36045427040", "40916036304", "44037977984", "44430326199" ]
[ "nonn" ]
9
1
1
[ "A377951", "A377953", "A378055", "A378056", "A378058", "A378059" ]
null
Amiram Eldar, Nov 15 2024
2024-11-15T12:56:13
oeisdata/seq/A378/A378059.seq
abf4200ba7815ee21c06cb0e3239957b
A378060
a(n) = binomial(n, floor((n-1)/2))^2.
[ "0", "1", "1", "9", "16", "100", "225", "1225", "3136", "15876", "44100", "213444", "627264", "2944656", "9018009", "41409225", "130873600", "590976100", "1914762564", "8533694884", "28210561600", "124408576656", "418151049316", "1828114918084", "6230734868736", "27043120090000", "93271169290000", "402335398890000" ]
[ "nonn", "easy", "walk" ]
29
0
4
[ "A037952", "A060150", "A337900", "A378060", "A378061" ]
null
Peter Luschny, Dec 03 2024
2024-12-09T05:47:22
oeisdata/seq/A378/A378060.seq
cdc09969f23d0ccbf2447c576ce57419
A378061
Triangle read by rows: T(n, k) = binomial(n + 1, (n - k)/2)^2*(k + 1)/(n + 1) if n - k is even, otherwise 0.
[ "1", "0", "1", "3", "0", "1", "0", "8", "0", "1", "20", "0", "15", "0", "1", "0", "75", "0", "24", "0", "1", "175", "0", "189", "0", "35", "0", "1", "0", "784", "0", "392", "0", "48", "0", "1", "1764", "0", "2352", "0", "720", "0", "63", "0", "1", "0", "8820", "0", "5760", "0", "1215", "0", "80", "0", "1", "19404", "0", "29700", "0", "12375", "0", "1925", "0", "99", "0", "1" ]
[ "nonn", "tabl" ]
19
0
4
[ "A000891", "A018224", "A145600", "A145601", "A145602", "A145603", "A378060", "A378061", "A378062" ]
null
Peter Luschny, Dec 07 2024
2024-12-08T17:22:02
oeisdata/seq/A378/A378061.seq
b1c247fd344a828b614bd43f79beabcd
A378062
Array read by ascending antidiagonals: A(n, k) = (n + 1)*binomial(2*k + n - 1, k - 1)^2 / (2*k + n - 1) for k > 0, and A(n, 0) = 0.
[ "0", "0", "1", "0", "1", "3", "0", "1", "8", "20", "0", "1", "15", "75", "175", "0", "1", "24", "189", "784", "1764", "0", "1", "35", "392", "2352", "8820", "19404", "0", "1", "48", "720", "5760", "29700", "104544", "226512", "0", "1", "63", "1215", "12375", "81675", "382239", "1288287", "2760615", "0", "1", "80", "1925", "24200", "196625", "1145144", "5010005", "16359200", "34763300" ]
[ "nonn", "tabl" ]
9
0
6
[ "A000891", "A005563", "A005565", "A145600", "A145601", "A145602", "A145603", "A378061", "A378062" ]
null
Peter Luschny, Dec 07 2024
2024-12-08T17:22:13
oeisdata/seq/A378/A378062.seq
573199bf477828fe51529cb340df3908
A378063
a(n) = (-2*n)^n * Euler(n, (n - 1)/(2*n)) for n >= 1, and a(0) = 1. Main diagonal of A378066.
[ "1", "1", "-3", "-26", "1185", "15376", "-2749355", "-49816976", "22790134017", "533858404096", "-498990299504499", "-14365294449638912", "23891962452055766497", "816609772823716089856", "-2201371244223771530940315", "-87139486416935710159898624", "355987789164484245477279893505" ]
[ "sign" ]
4
0
3
[ "A378063", "A378066" ]
null
Peter Luschny, Nov 17 2024
2024-11-18T13:01:12
oeisdata/seq/A378/A378063.seq
ec0b3b6f892727f35567690a9a96a5ba
A378064
a(n) = 5*n^4 - 6*n^2 + 1. Column 4 of A378066.
[ "1", "0", "57", "352", "1185", "2976", "6265", "11712", "20097", "32320", "49401", "72480", "102817", "141792", "190905", "251776", "326145", "415872", "522937", "649440", "797601", "969760", "1168377", "1396032", "1655425", "1949376", "2280825", "2652832", "3068577", "3531360", "4044601", "4611840", "5236737", "5923072" ]
[ "nonn" ]
6
0
3
[ "A378064", "A378066" ]
null
Peter Luschny, Nov 17 2024
2024-11-19T00:51:28
oeisdata/seq/A378/A378064.seq
fd34de41381577e39b6e0e6fe2e694fb
A378065
a(n) = (-10)^n * Euler(n, 2/5). Row 5 of A378066.
[ "1", "1", "-24", "-74", "2976", "15376", "-906624", "-6563024", "514546176", "4789470976", "-469222938624", "-5338232282624", "627559296638976", "8437702651826176", "-1157248322241921024", "-17953287144063002624", "2814090582404042981376", "49478116534660975230976", "-8724885890905288434253824" ]
[ "sign" ]
7
0
3
[ "A378065", "A378066" ]
null
Peter Luschny, Nov 17 2024
2024-11-18T13:01:09
oeisdata/seq/A378/A378065.seq
21d9e268c73131b63cc148fa94c52e6a
A378066
Array read by ascending antidiagonals: A(n, k) = (-2*n)^k * Euler(k, (n - 1)/(2*n)) for n >= 1 and A(0, k) = 1.
[ "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "-3", "-2", "1", "1", "1", "-8", "-11", "0", "1", "1", "1", "-15", "-26", "57", "16", "1", "1", "1", "-24", "-47", "352", "361", "0", "1", "1", "1", "-35", "-74", "1185", "1936", "-2763", "-272", "1", "1", "1", "-48", "-107", "2976", "6241", "-38528", "-24611", "0", "1" ]
[ "sign", "tabl" ]
11
0
13
[ "A000012", "A000810", "A000813", "A005563", "A080663", "A081658", "A155585", "A188458", "A377666", "A378063", "A378064", "A378065", "A378066" ]
null
Peter Luschny, Nov 15 2024
2024-11-18T13:01:19
oeisdata/seq/A378/A378066.seq
c1965437143234f3534b5ebd757f9f2b
A378067
Triangle read by rows: T(n, k) is the number of walks of length n with unit steps in all four directions (NSWE) starting at (0, 0), staying in the upper plane (y >= 0), and ending on the vertical line x = 0 if k = 0, or on the line x = k or x = -(n + 1 - k) if k > 0.
[ "1", "1", "2", "4", "3", "3", "9", "10", "6", "10", "36", "25", "20", "20", "25", "100", "101", "55", "50", "55", "101", "400", "301", "231", "126", "126", "231", "301", "1225", "1226", "742", "490", "294", "490", "742", "1226", "4900", "3921", "3144", "1632", "1008", "1008", "1632", "3144", "3921", "15876", "15877", "10593", "7137", "3348", "2592", "3348", "7137", "10593", "15877" ]
[ "nonn", "tabl", "walk" ]
19
0
3
[ "A001700", "A018224", "A052174", "A378067", "A378069", "A379822", "A380121" ]
null
Peter Luschny, Dec 08 2024
2025-01-17T07:04:27
oeisdata/seq/A378/A378067.seq
1544b3c2be61a2c180a6354d97ec79eb
A378068
Table read by row: T(n, k) = Sum_{j=0..k} A217831(n, j). Partial row sums of Euclid's triangle.
[ "0", "1", "2", "0", "1", "1", "0", "1", "2", "2", "0", "1", "1", "2", "2", "0", "1", "2", "3", "4", "4", "0", "1", "1", "1", "1", "2", "2", "0", "1", "2", "3", "4", "5", "6", "6", "0", "1", "1", "2", "2", "3", "3", "4", "4", "0", "1", "2", "2", "3", "4", "4", "5", "6", "6", "0", "1", "1", "2", "2", "2", "2", "3", "3", "4", "4", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "10", "0", "1", "1", "1", "1", "2", "2", "3", "3", "3", "3", "4", "4" ]
[ "nonn", "tabl" ]
10
0
3
[ "A000010", "A092790", "A217831", "A378068" ]
null
Peter Luschny, Dec 26 2024
2024-12-26T16:36:09
oeisdata/seq/A378/A378068.seq
884a3d1be1b11678cfa663f6b2b503f4
A378069
a(n) = Sum_{k=0..n} binomial(n, floor(k/2 - 1/2)) * binomial(n, ceiling(k/2 - 1/2)).
[ "0", "1", "3", "13", "45", "181", "658", "2605", "9705", "38251", "144606", "569317", "2173262", "8556822", "32890068", "129565485", "500583105", "1973295775", "7654363750", "30194784763", "117497078842", "463820452602", "1809540528588", "7147843461733", "27946421773270", "110458073192026", "432648616232028" ]
[ "nonn", "easy" ]
3
0
3
[ "A005566", "A007318", "A378069", "A378070" ]
null
Peter Luschny, Dec 14 2024
2024-12-14T18:18:40
oeisdata/seq/A378/A378069.seq
b20adb342ee1a22badfb2aaf42e7f7e5
A378070
a(n) = binomial(n - 1, ceiling(n/2)) * binomial(n - 1, ceiling(n/2) - 1).
[ "1", "0", "1", "2", "9", "24", "100", "300", "1225", "3920", "15876", "52920", "213444", "731808", "2944656", "10306296", "41409225", "147232800", "590976100", "2127513960", "8533694884", "31031617760", "124408576656", "456164781072", "1828114918084", "6749962774464", "27043120090000", "100445874620000", "402335398890000" ]
[ "nonn", "easy" ]
29
0
4
[ "A007318", "A060150", "A135389", "A378060", "A378070" ]
null
Peter Luschny, Dec 13 2024
2024-12-15T05:26:59
oeisdata/seq/A378/A378070.seq
8bdc0ff73826d8133cff81d60adc3b54
A378071
a(n) = denominator((4^(2*n+1)*n!^2)/((2*n+3)*(2*n)!)).
[ "3", "5", "21", "45", "385", "819", "3465", "7293", "122265", "255255", "1062347", "2204475", "18253053", "37702175", "155451825", "319929885", "10518906825", "21585857535", "88482569175", "181144476975", "1481850184815", "3027700543725", "12361581411855", "25214881603275", "411156946959525", "837470267650107" ]
[ "nonn", "frac" ]
8
0
1
[ "A102557", "A378071" ]
null
Peter Luschny, Dec 05 2024
2024-12-05T19:19:16
oeisdata/seq/A378/A378071.seq
e8546d080991c3308914c46bff8ff963
A378072
Number of elements in the completion of the Bruhat order on B_n.
[ "1", "2", "10", "132", "4824", "493600" ]
[ "nonn", "more" ]
33
0
2
[ "A000165", "A005130", "A005158", "A378072" ]
null
Ludovic Schwob, Nov 16 2024
2024-11-19T02:19:19
oeisdata/seq/A378/A378072.seq
62100149bab37612c644cb84411c9d24
A378073
Positive integers that are digitally balanced in some integer base b >= 2.
[ "2", "9", "10", "11", "12", "15", "19", "21", "35", "37", "38", "41", "42", "44", "49", "50", "52", "56", "75", "78", "99", "108", "114", "120", "135", "139", "141", "142", "147", "149", "150", "153", "154", "156", "163", "165", "166", "169", "170", "172", "177", "178", "180", "184", "195", "197", "198", "201", "202", "204", "209", "210", "212", "216", "225", "226", "228" ]
[ "nonn", "base" ]
16
1
1
[ "A049364", "A061845", "A065963", "A378000", "A378073", "A378080", "A378104", "A378191" ]
null
Paolo Xausa, Nov 16 2024
2024-11-21T09:05:22
oeisdata/seq/A378/A378073.seq
58e80d572f3e76414524c463b54a0e19
A378074
Number of embeddings on the sphere of 2-connected homeomorphically irreducible planar graphs with n nodes.
[ "0", "0", "0", "1", "2", "9", "47", "420", "4673", "63253", "927238", "14342093", "229607392", "3776227106", "63482545872", "1087322656758", "18927037827561" ]
[ "nonn", "more" ]
7
1
5
[ "A000944", "A034889", "A187927", "A378074", "A378075", "A378076" ]
null
Andrew Howroyd, Nov 15 2024
2024-11-15T19:39:05
oeisdata/seq/A378/A378074.seq
8106aba6420fd7c3d3ce7d5330044384
A378075
Triangle read by rows: T(n,k) is the number of embeddings on the sphere of 2-connected homeomorphically irreducible planar graphs with n nodes and k faces, k=4..2n-4.
[ "1", "0", "1", "1", "0", "1", "3", "3", "2", "0", "0", "3", "11", "18", "10", "5", "0", "0", "3", "19", "77", "134", "123", "50", "14", "0", "0", "0", "13", "146", "603", "1280", "1420", "883", "278", "50", "0", "0", "0", "8", "162", "1409", "6030", "13781", "18404", "14570", "6884", "1772", "233", "0", "0", "0", "0", "83", "1809", "15225", "64502", "158717", "240841", "233286", "144005", "55444", "12077", "1249" ]
[ "nonn", "tabf" ]
11
4
7
[ "A212438", "A342060", "A378074", "A378075", "A378076", "A378077" ]
null
Andrew Howroyd, Nov 15 2024
2024-11-15T19:39:01
oeisdata/seq/A378/A378075.seq
bf8715655b425e66b747b66157ec992c
A378076
Number of embeddings on the sphere of 2-connected homeomorphically irreducible planar graphs with n edges.
[ "1", "0", "1", "2", "3", "6", "16", "37", "100", "293", "888", "2822", "9305", "31274", "106972", "370828", "1298058", "4582413", "16289759", "58259600", "209465186" ]
[ "nonn", "more" ]
5
6
4
[ "A002840", "A006407", "A187928", "A378075", "A378076" ]
null
Andrew Howroyd, Nov 15 2024
2024-11-15T19:38:55
oeisdata/seq/A378/A378076.seq
7a9bd676a2aec1b27333c9783ff42148
A378077
Triangle read by rows: T(n,k) is the number of embeddings on the sphere of planar graphs with n vertices and k faces having connectivity exactly 2 and minimum vertex degree at least 3, k=6..2n-5.
[ "1", "1", "1", "3", "7", "2", "1", "8", "35", "60", "47", "12", "0", "5", "72", "307", "647", "652", "325", "59", "0", "3", "86", "776", "3395", "7647", "9582", "6654", "2442", "368", "0", "0", "45", "1041", "9091", "38876", "94278", "136628", "121204", "64232", "18916", "2363", "0", "0", "18", "827", "14407", "111076", "468211", "1192511", "1937266", "2049784", "1409199", "607746", "150161", "16253" ]
[ "nonn", "tabf" ]
8
6
4
[ "A187927", "A187928", "A378075", "A378077" ]
null
Andrew Howroyd, Nov 15 2024
2024-11-15T19:38:51
oeisdata/seq/A378/A378077.seq
3a83abb91ae74e084fd4ba28cb973e27
A378078
Number of noncrossing trees with n edges and all nodes having degree at most 3.
[ "1", "1", "3", "12", "50", "219", "987", "4552", "21366", "101730", "490094", "2384520", "11699844", "57825103", "287611755", "1438536144", "7230782414", "36506547918", "185047345050", "941359362760", "4804468999932", "24593960996814", "126239765780606", "649610643221616", "3350542070046300", "17318377059738820" ]
[ "nonn" ]
8
0
3
[ "A001764", "A122871", "A378078", "A378079" ]
null
Andrew Howroyd, Nov 21 2024
2024-11-21T22:26:26
oeisdata/seq/A378/A378078.seq
e5e9eb852d38d5dbd8b0147755636b8b
A378079
Number of series-reduced noncrossing trees with n edges.
[ "1", "1", "0", "4", "5", "33", "91", "408", "1485", "6195", "24838", "103752", "432796", "1834140", "7815900", "33591376", "145197017", "631281591", "2757917260", "12102728740", "53321334381", "235768155073", "1045889996047", "4653534540816", "20761857325000", "92862669150004", "416316199107096", "1870414803490240" ]
[ "nonn" ]
6
0
4
[ "A000014", "A001764", "A030980", "A378078", "A378079" ]
null
Andrew Howroyd, Nov 21 2024
2024-11-21T22:26:22
oeisdata/seq/A378/A378079.seq
e9c2f66c071995012cd3f385ce2cfa41
A378080
Nonnegative integers that are not digitally balanced in any integer base b >= 2.
[ "0", "1", "3", "4", "5", "6", "7", "8", "13", "14", "16", "17", "18", "20", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "36", "39", "40", "43", "45", "46", "47", "48", "51", "53", "54", "55", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74", "76", "77", "79", "80", "81", "82", "83", "84", "85", "86", "87" ]
[ "nonn", "base" ]
16
1
3
[ "A378000", "A378073", "A378080", "A378104", "A378191" ]
null
Paolo Xausa, Nov 16 2024
2024-11-21T09:05:27
oeisdata/seq/A378/A378080.seq
2c59f7e4082e4d222bb1a665043d1eb2
A378081
Primes that remain prime if any two of their digits are deleted.
[ "223", "227", "233", "257", "277", "337", "353", "373", "523", "557", "577", "727", "733", "757", "773", "1117", "1171", "4111" ]
[ "nonn", "base", "more" ]
32
1
1
[ "A019546", "A051362", "A226108", "A378081" ]
null
Enrique Navarrete, Nov 15 2024
2024-11-20T09:59:40
oeisdata/seq/A378/A378081.seq
34be6bfa92160fb2319963d61fb8b67e
A378082
Terms appearing only once in A377783 = least nonsquarefree number > prime(n).
[ "12", "16", "18", "20", "24", "40", "48", "54", "60", "63", "68", "72", "75", "80", "84", "90", "98", "108", "112", "116", "128", "132", "150", "152", "160", "164", "168", "175", "180", "184", "192", "196", "198", "200", "212", "224", "228", "232", "234", "240", "242", "252", "260", "264", "270", "272", "279", "294", "308", "312", "315", "320", "332", "338", "348" ]
[ "nonn" ]
11
1
1
[ "A000040", "A001223", "A005117", "A013928", "A013929", "A036263", "A053797", "A053806", "A057627", "A061398", "A061399", "A068360", "A068361", "A070321", "A071403", "A072284", "A078147", "A112925", "A112926", "A112929", "A120327", "A120992", "A224363", "A337030", "A376593", "A377430", "A377431", "A377703", "A377783", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378082", "A378083", "A378084", "A378086" ]
null
Gus Wiseman, Nov 20 2024
2024-12-05T10:47:46
oeisdata/seq/A378/A378082.seq
254316e60018465fbb7406f5d173bc95
A378083
Nonsquarefree numbers appearing exactly twice in A377783 (least nonsquarefree number > prime(n)).
[ "4", "8", "32", "44", "104", "140", "284", "464", "572", "620", "644", "824", "860", "1232", "1292", "1304", "1484", "1700", "1724", "1880", "2084", "2132", "2240", "2312", "2384", "2660", "2732", "2804", "3392", "3464", "3560", "3920", "3932", "4004", "4220", "4244", "4424", "4640", "4724", "5012", "5444", "5480", "5504", "5660", "6092", "6200" ]
[ "nonn" ]
5
1
1
[ "A000040", "A001223", "A005117", "A013928", "A013929", "A036263", "A053797", "A053806", "A057627", "A061398", "A061399", "A068360", "A068361", "A070321", "A071403", "A072284", "A078147", "A112925", "A112926", "A112929", "A120327", "A120992", "A224363", "A337030", "A377430", "A377431", "A377703", "A377783", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378082", "A378083", "A378084", "A378086" ]
null
Gus Wiseman, Nov 23 2024
2024-11-24T22:49:09
oeisdata/seq/A378/A378083.seq
c632663bf92b36445f99778416c60ed3
A378084
Nonsquarefree numbers not appearing in A377783 (least nonsquarefree number > prime(n)).
[ "9", "25", "27", "28", "36", "45", "49", "50", "52", "56", "64", "76", "81", "88", "92", "96", "99", "100", "117", "120", "121", "124", "125", "126", "135", "136", "144", "147", "148", "153", "156", "162", "169", "171", "172", "176", "188", "189", "204", "207", "208", "216", "220", "225", "236", "243", "244", "245", "248", "250", "256", "261", "268", "275", "276", "280" ]
[ "nonn" ]
5
1
1
[ "A000040", "A001223", "A005117", "A013929", "A036263", "A053797", "A053806", "A061398", "A061399", "A068360", "A068361", "A070321", "A072284", "A078147", "A112925", "A112926", "A120327", "A162966", "A224363", "A337030", "A376593", "A377046", "A377050", "A377430", "A377431", "A377783", "A377784", "A378032", "A378033", "A378037", "A378038", "A378039", "A378040", "A378082", "A378083", "A378084", "A378086" ]
null
Gus Wiseman, Nov 23 2024
2024-11-24T22:49:04
oeisdata/seq/A378/A378084.seq
e13d36533b4653ca39bb132997f9d632
A378085
First differences of A070321 (greatest squarefree number <= n).
[ "1", "1", "0", "2", "1", "1", "0", "0", "3", "1", "0", "2", "1", "1", "0", "2", "0", "2", "0", "2", "1", "1", "0", "0", "3", "0", "0", "3", "1", "1", "0", "2", "1", "1", "0", "2", "1", "1", "0", "2", "1", "1", "0", "0", "3", "1", "0", "0", "0", "4", "0", "2", "0", "2", "0", "2", "1", "1", "0", "2", "1", "0", "0", "3", "1", "1", "0", "2", "1", "1", "0", "2", "1", "0", "0", "3", "1", "1", "0", "0", "3", "1", "0", "2", "1", "1", "0" ]
[ "nonn" ]
6
1
4
[ "A005117", "A007674", "A013928", "A013929", "A020754", "A020755", "A045882", "A053797", "A053806", "A067535", "A068781", "A070321", "A072284", "A073247", "A073248", "A078147", "A112925", "A112926", "A120327", "A280892", "A376593", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378038", "A378039", "A378085", "A378087" ]
null
Gus Wiseman, Dec 04 2024
2024-12-04T10:16:35
oeisdata/seq/A378/A378085.seq
e6d4fc13124b455914b2dbdbcda68967
A378086
Number of nonsquarefree numbers < prime(n).
[ "0", "0", "1", "1", "3", "4", "5", "6", "7", "11", "11", "13", "14", "14", "16", "20", "22", "23", "25", "26", "27", "29", "31", "33", "36", "39", "39", "40", "41", "42", "49", "50", "53", "53", "57", "58", "61", "63", "64", "68", "70", "71", "74", "75", "76", "77", "81", "84", "86", "87", "88", "90", "91", "97", "99", "101", "103", "104", "107", "109", "109", "113", "119", "120", "121" ]
[ "nonn" ]
10
1
5
[ "A000040", "A001223", "A005117", "A013928", "A013929", "A014689", "A036263", "A046933", "A053797", "A053806", "A057627", "A061398", "A061399", "A065890", "A068360", "A068361", "A070321", "A071403", "A072284", "A076259", "A078147", "A112925", "A112926", "A120327", "A224363", "A337030", "A373198", "A376593", "A377049", "A377783", "A377784", "A378032", "A378033", "A378034", "A378036", "A378037", "A378038", "A378039", "A378040", "A378082", "A378084", "A378086" ]
null
Gus Wiseman, Dec 04 2024
2024-12-05T12:06:50
oeisdata/seq/A378/A378086.seq
59e799b4767ccdfc8dca8e268725a0ec
A378087
First-differences of A067535 (least positive integer >= n that is squarefree).
[ "1", "1", "2", "0", "1", "1", "3", "0", "0", "1", "2", "0", "1", "1", "2", "0", "2", "0", "2", "0", "1", "1", "3", "0", "0", "3", "0", "0", "1", "1", "2", "0", "1", "1", "2", "0", "1", "1", "2", "0", "1", "1", "3", "0", "0", "1", "4", "0", "0", "0", "2", "0", "2", "0", "2", "0", "1", "1", "2", "0", "1", "3", "0", "0", "1", "1", "2", "0", "1", "1", "2", "0", "1", "3", "0", "0", "1", "1", "3", "0", "0", "1", "2", "0", "1", "1", "2" ]
[ "nonn" ]
8
1
3
[ "A000015", "A000040", "A001223", "A005117", "A007674", "A007675", "A013928", "A013929", "A020754", "A036263", "A045882", "A053797", "A053806", "A061398", "A061399", "A067535", "A068360", "A068361", "A068781", "A070321", "A072284", "A073247", "A073248", "A078147", "A112926", "A120327", "A224363", "A280892", "A376593", "A377780", "A377783", "A377784", "A378033", "A378036", "A378037", "A378038", "A378039", "A378040", "A378084", "A378085", "A378087" ]
null
Gus Wiseman, Nov 20 2024
2024-11-22T11:08:25
oeisdata/seq/A378/A378087.seq
2051e270f9f28d296f020c9b7054a428
A378088
Repdigit untouchable numbers.
[ "2", "5", "88", "66666", "222222", "6666666" ]
[ "nonn", "base", "hard", "more" ]
6
1
1
[ "A005114", "A010785", "A378088" ]
null
Shyam Sunder Gupta, Nov 16 2024
2024-12-01T11:36:59
oeisdata/seq/A378/A378088.seq
a1e6875e36dad249e57c2357488de32a
A378089
Irregular triangle read by rows in which row n lists the numbers k such that phi(k)/tau(k) = n.
[ "1", "3", "8", "10", "18", "24", "30", "5", "9", "15", "28", "40", "72", "84", "90", "120", "7", "21", "26", "56", "70", "78", "108", "126", "168", "210", "34", "45", "52", "102", "140", "156", "252", "360", "420", "11", "33", "88", "110", "198", "264", "330", "13", "35", "39", "63", "76", "104", "105", "130", "228", "234", "280", "312", "390", "504", "540", "630", "840", "58", "98", "174", "294" ]
[ "nonn", "tabf" ]
8
1
2
[ "A000005", "A000010", "A020488", "A020491", "A062516", "A063469", "A063470", "A112954", "A112955", "A175667", "A378089" ]
null
Mohammed Yaseen, Nov 16 2024
2024-11-18T22:30:39
oeisdata/seq/A378/A378089.seq
9da95c0300dc230e992922a0494058f5
A378090
E.g.f. satisfies A(x) = exp(x * (1-x)^2 * A(x)) / (1-x)^3.
[ "1", "4", "23", "181", "1889", "25411", "427615", "8736337", "210911489", "5882285971", "186121646831", "6585885144697", "257640988064641", "11039620794801691", "514147575711741119", "25858553659455655201", "1396703647943164718081", "80633376290492591578147", "4954794080385073122030799" ]
[ "nonn" ]
15
0
2
[ "A323772", "A352410", "A378090", "A378091" ]
null
Seiichi Manyama, Nov 16 2024
2025-03-24T22:33:52
oeisdata/seq/A378/A378090.seq
96cebd3eb6545dd07778ea21bc2ae295
A378091
E.g.f. satisfies A(x) = exp(x * (1-x)^3 * A(x)) / (1-x)^4.
[ "1", "5", "33", "280", "3009", "40456", "670351", "13428794", "318341841", "8747362540", "273595272231", "9595433139238", "372786185735497", "15885841209363152", "736549352642825247", "36906793949098033906", "1987212351128733260577", "114415986259681057007956", "7014281833059332148174007" ]
[ "nonn" ]
15
0
2
[ "A323772", "A352410", "A378090", "A378091" ]
null
Seiichi Manyama, Nov 16 2024
2025-03-24T22:34:09
oeisdata/seq/A378/A378091.seq
ff0124dd8f905d6f7451ac6152e5f8bc
A378092
E.g.f. satisfies A(x) = exp( x * (1-x) * A(x)^2 ) / (1-x).
[ "1", "2", "11", "118", "1993", "46386", "1376059", "49601014", "2104366513", "102717184546", "5670357524011", "349304240222070", "23754501885783673", "1767641331001915474", "142868173684094891803", "12463599550013379095926", "1167281368458948415748833", "116814664082977998388994370", "12440156205235958837516345419" ]
[ "nonn" ]
10
0
2
[ "A352410", "A378041", "A378092", "A378093" ]
null
Seiichi Manyama, Nov 16 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378092.seq
198839a61471887e9bbf7cede8be6d94
A378093
E.g.f. satisfies A(x) = exp( x * (1-x)^2 * A(x)^3 ) / (1-x).
[ "1", "2", "13", "187", "4421", "145381", "6106885", "312010217", "18775791529", "1300609323577", "101932831136801", "8917429459192717", "861423205666601869", "91071085791088039781", "10459294205668851438589", "1296711971347861868098561", "172604468588739615868724945", "24551969347625035312300681969" ]
[ "nonn" ]
11
0
2
[ "A352410", "A363478", "A378092", "A378093" ]
null
Seiichi Manyama, Nov 16 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378093.seq
9fdb60a595e5b02fb0626fece83f5548
A378094
E.g.f. satisfies A(x) = exp( x^2 * A(x) / (1-x) ) / (1-x).
[ "1", "1", "4", "24", "204", "2220", "29640", "469560", "8623440", "180306000", "4231815840", "110217270240", "3155551439040", "98529432281280", "3332752472649600", "121416875166787200", "4740431035737196800", "197475789694088505600", "8743499113411321459200", "410050296758706725721600" ]
[ "nonn" ]
14
0
3
[ "A352410", "A371038", "A378094", "A378095" ]
null
Seiichi Manyama, Nov 16 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378094.seq
5df38d3544ec8763c71da9d2d64859b1
A378095
E.g.f. satisfies A(x) = exp( x^3 * A(x) / (1-x)^2 ) / (1-x).
[ "1", "1", "2", "12", "120", "1320", "16200", "234360", "3991680", "77535360", "1678924800", "40142995200", "1053264643200", "30109980700800", "931249403884800", "30979797430982400", "1103292884684390400", "41889177988142284800", "1689202127352118579200", "72105273328152166502400" ]
[ "nonn" ]
12
0
3
[ "A352410", "A378094", "A378095" ]
null
Seiichi Manyama, Nov 16 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378095.seq
81b20485d1c557c418edea3b2ba4e962
A378096
Decimal expansion of Product_{k>=2} (1 - 1/A047233(k)^2).
[ "8", "7", "5", "1", "8", "0", "0", "6", "8", "5", "7", "3", "0", "1", "8", "1", "3", "4", "6", "6", "0", "5", "4", "0", "8", "3", "0", "0", "8", "2", "7", "3", "9", "4", "7", "0", "4", "3", "2", "8", "7", "6", "1", "7", "4", "3", "9", "8", "4", "9", "3", "3", "4", "1", "5", "4", "4", "2", "4", "0", "7", "5", "2", "2", "9", "0", "1", "9", "9", "2", "1", "5", "3", "9", "4", "3", "0", "2", "6", "9", "4", "4", "7", "0", "9", "3", "5", "0", "1", "4", "1", "5", "2", "0", "4", "5", "9", "7", "9", "5", "3", "5", "2", "5", "3" ]
[ "cons", "nonn" ]
15
0
1
[ "A001318", "A007310", "A047233", "A378096" ]
null
Frank Richter, Nov 16 2024
2024-11-17T07:18:02
oeisdata/seq/A378/A378096.seq
27da328353ae7859808cc67847d9c7da
A378097
Products of 6 distinct primes that are sandwiched between twin prime numbers.
[ "43890", "51870", "84630", "102102", "140070", "149730", "153510", "168630", "224070", "251790", "269178", "281190", "308490", "316470", "317730", "322770", "355110", "376530", "381990", "383838", "389298", "404430", "432390", "434010", "459030", "467670", "486330", "487830", "496230", "506730", "520410", "531570", "545790", "552090", "560490", "573342", "576030", "583338" ]
[ "nonn" ]
18
1
1
[ "A014574", "A067885", "A083207", "A353022", "A376380", "A378097" ]
null
Massimo Kofler, Nov 16 2024
2024-12-03T12:23:13
oeisdata/seq/A378/A378097.seq
04758cf1af56a7d5959f1306df5e4802
A378098
Lexicographically earliest sequence of distinct positive integers such that a(a(n)) shares a factor with a(a(n)-1).
[ "2", "4", "5", "10", "6", "8", "9", "12", "14", "16", "13", "26", "18", "15", "20", "22", "19", "38", "24", "21", "27", "30", "25", "35", "28", "32", "34", "36", "23", "46", "33", "39", "42", "40", "44", "48", "41", "82", "50", "45", "51", "54", "47", "94", "52", "56", "49", "63", "57", "60", "55", "65", "58", "62", "64", "66", "68", "70", "61", "122", "72", "69", "75", "78", "74", "76", "71", "142", "80", "84", "77", "88", "79", "158", "86", "90", "81", "87", "93", "96", "92", "98", "85", "95", "100", "102", "99", "105", "91", "104" ]
[ "nonn" ]
9
1
1
[ "A027746", "A064413", "A121053", "A378030", "A378098" ]
null
Scott R. Shannon, Nov 16 2024
2024-11-17T07:16:05
oeisdata/seq/A378/A378098.seq
ad432d3d6e5492a8ea517f50a9328901
A378099
The smallest number whose sum of proper divisors (aliquot parts) is the repunit number (10^n - 1)/9, denoted by R_n.
[ "2", "21", "321", "7721", "184729", "185145", "21110729", "54929017", "134099385", "3331670169" ]
[ "nonn", "hard", "more" ]
13
1
1
[ "A001065", "A002275", "A378099" ]
null
Shyam Sunder Gupta, Nov 16 2024
2024-12-01T11:37:17
oeisdata/seq/A378/A378099.seq
38ab62717878d6f2c644f08166873a6d
A378100
Number of involutions in the symmetric group S_n with at least one fixed point.
[ "0", "1", "1", "4", "7", "26", "61", "232", "659", "2620", "8551", "35696", "129757", "568504", "2255345", "10349536", "44179711", "211799312", "962854399", "4809701440", "23103935021", "119952692896", "605135328337", "3257843882624", "17175956434375", "95680443760576", "525079354619951", "3020676745975552" ]
[ "nonn", "easy" ]
25
0
4
[ "A000085", "A000166", "A002467", "A099174", "A123023", "A378100" ]
null
Maniru Ibrahim, Nov 16 2024
2025-01-28T08:36:22
oeisdata/seq/A378/A378100.seq
b34a1036d2381dd19fe5a2cdaa582ceb