cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 32 results. Next

A050368 Number of ways to factor n into distinct factors with 2 kinds of 2, 3 kinds of 3, ...

Original entry on oeis.org

1, 2, 3, 5, 5, 12, 7, 16, 12, 20, 11, 39, 13, 28, 30, 42, 17, 60, 19, 65, 42, 44, 23, 126, 35, 52, 55, 91, 29, 150, 31, 116, 66, 68, 70, 219, 37, 76, 78, 210, 41, 210, 43, 143, 150, 92, 47, 378, 70, 170, 102, 169, 53, 290, 110, 294, 114, 116, 59, 570, 61, 124, 210
Offset: 1

Views

Author

Christian G. Bower, Oct 15 1999

Keywords

Links

Crossrefs

Cf. A045778, A050367.

Programs

  • PARI
    seq(n)={my(v=vector(n, k, k==1)); for(k=2, n, my(m=logint(n,k), p=(1 + x + O(x*x^m))^k, w=vector(n)); for(i=0, m, w[k^i]=polcoef(p,i)); v=dirmul(v,w)); v} \\ Andrew Howroyd, Oct 27 2019

Formula

Dirichlet g.f.: Product_{n>=2}((1+1/n^s)^n).

A329125 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k^2).

Original entry on oeis.org

1, 4, 9, 26, 25, 72, 49, 148, 126, 200, 121, 522, 169, 392, 450, 843, 289, 1152, 361, 1450, 882, 968, 529, 3420, 950, 1352, 1623, 2842, 841, 4500, 961, 4632, 2178, 2312, 2450, 9126, 1369, 2888, 3042, 9500, 1681, 8820, 1849, 7018, 7200, 4232, 2209, 21267, 3626, 8800, 5202, 9802, 2809
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 05 2019

Keywords

Crossrefs

Cf. A001055, A050367, A329124.

A329800 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(2^(k - 1)).

Original entry on oeis.org

1, 2, 4, 11, 16, 40, 64, 148, 266, 544, 1024, 2156, 4096, 8320, 16448, 33089, 65536, 131732, 262144, 525488, 1048832, 2099200, 4194304, 8393648, 16777352, 33562624, 67109908, 134234816, 268435456, 536906368, 1073741824, 2147550702, 4294971392, 8590065664, 17179870208
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 21 2019

Keywords

Crossrefs

Cf. A011782, A050367, A318949.

A343283 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k^3).

Original entry on oeis.org

1, 8, 27, 100, 125, 432, 343, 1144, 1107, 2000, 1331, 6156, 2197, 5488, 6750, 12906, 4913, 20520, 6859, 28500, 18522, 21296, 12167, 80136, 23500, 35152, 43020, 78204, 24389, 135000, 29791, 141848, 71874, 78608, 85750, 320760, 50653, 109744, 118638, 371000, 68921, 370440, 79507
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 10 2021

Keywords

Crossrefs

Cf. A000578, A001055, A023872, A050367, A329125, A343284, A343285, A343286, A343287, A343288, A343289.

A343284 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k^4).

Original entry on oeis.org

1, 16, 81, 392, 625, 2592, 2401, 9008, 9882, 20000, 14641, 73224, 28561, 76832, 101250, 202660, 83521, 368064, 130321, 565000, 388962, 468512, 279841, 1901232, 586250, 913952, 1154763, 2170504, 707281, 4050000, 923521, 4453520, 2371842, 2672672, 3001250, 11432664, 1874161, 4170272
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 10 2021

Keywords

Crossrefs

Cf. A000583, A001055, A023873, A050367, A329125, A343283, A343285, A343286, A343287, A343288, A343289.

A343285 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(k^5).

Original entry on oeis.org

1, 32, 243, 1552, 3125, 15552, 16807, 71520, 88695, 200000, 161051, 874800, 371293, 1075648, 1518750, 3214984, 1419857, 6617376, 2476099, 11250000, 8168202, 10307264, 6436343, 45372960, 14650000, 23762752, 31118904, 60505200, 20511149, 121500000, 28629151, 141263008, 78270786, 90870848
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 10 2021

Keywords

Crossrefs

Cf. A000584, A001055, A023874, A050367, A329125, A343283, A343284, A343286, A343287, A343288, A343289.

A344247 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(3^(k-1)).

Original entry on oeis.org

1, 3, 9, 33, 81, 270, 729, 2278, 6606, 19926, 59049, 178173, 531441, 1596510, 4783698, 14356023, 43046721, 129162168, 387420489, 1162323189, 3486790962, 10460530350, 31381059609, 94143738789, 282429539802, 847290203766, 2541865887543, 7625602292013, 22876792454961, 68630391912807
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2021

Keywords

Crossrefs

Cf. A001055, A050367, A329800, A344248, A344249, A344250, A344251, A344252, A344253.

A344248 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(4^(k-1)).

Original entry on oeis.org

1, 4, 16, 74, 256, 1088, 4096, 16660, 65672, 263168, 1048576, 4199584, 16777216, 67125248, 268439552, 1073810115, 4294967296, 17180148256, 68719476736, 274878974464, 1099511693312, 4398050705408, 17592186044416, 70368761297216, 281474976743552, 1125899973951488, 4503599628419888
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2021

Keywords

Crossrefs

Cf. A001055, A050367, A329800, A344247, A344249, A344250, A344251, A344252, A344253.

A344249 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(5^(k-1)).

Original entry on oeis.org

1, 5, 25, 140, 625, 3250, 15625, 78785, 390950, 1956250, 9765625, 48847250, 244140625, 1220781250, 6103531250, 30517978570, 152587890625, 762941486000, 3814697265625, 19073496181250, 95367432031250, 476837207031250, 2384185791015625, 11920929201625875, 59604644775586250
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2021

Keywords

Crossrefs

Cf. A001055, A050367, A329800, A344247, A344248, A344250, A344251, A344252, A344253.

A344250 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(6^(k-1)).

Original entry on oeis.org

1, 6, 36, 237, 1296, 7992, 46656, 281288, 1680282, 10085472, 60466176, 362852244, 2176782336, 13060973952, 78364210752, 470186692290, 2821109907456, 16926669806364, 101559956668416, 609359800783824, 3656158441742592, 21936951003174912, 131621703842267136
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2021

Keywords

Crossrefs

Cf. A001055, A050367, A329800, A344247, A344248, A344249, A344251, A344252, A344253.
Showing 1-10 of 32 results. Next

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