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 1-7 of 7 results.

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

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

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

A344251 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(7^(k-1)).

Original entry on oeis.org

1, 7, 49, 371, 2401, 17150, 117649, 826028, 5766026, 40370414, 282475249, 1977462571, 13841287201, 96889833950, 678223190498, 4747567343554, 33232930569601, 232630555172932, 1628413597910449, 11398895468739163, 79792266303376802, 558545866060610750
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2021

Keywords

Crossrefs

A344252 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(8^(k-1)).

Original entry on oeis.org

1, 8, 64, 548, 4096, 33280, 262144, 2101368, 16779296, 134250496, 1073741824, 8590231808, 68719476736, 549757911040, 4398046773248, 35184389016138, 281474976710656, 2251799950016768, 18014398509481984, 144115189151842304, 1152921504623624192, 9223372045444710400
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2021

Keywords

Crossrefs

A344253 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^(9^(k-1)).

Original entry on oeis.org

1, 9, 81, 774, 6561, 59778, 531441, 4789695, 43050042, 387479538, 3486784401, 31381653744, 282429536481, 2541870611298, 22876792986402, 205891175440755, 1853020188851841, 16677182091899916, 150094635296999121, 1350851721164854704, 12157665459099975522, 109418989162893418818
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2021

Keywords

Crossrefs

A344268 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(5^(k-1)).

Original entry on oeis.org

1, 5, 25, 135, 625, 3250, 15625, 78760, 390925, 1956250, 9765625, 48847125, 244140625, 1220781250, 6103531250, 30517977755, 152587890625, 762941485875, 3814697265625, 19073496178125, 95367432031250, 476837207031250, 2384185791015625, 11920929201609625, 59604644775585625, 298023225097656250
Offset: 1

Views

Author

Ilya Gutkovskiy, May 13 2021

Keywords

Crossrefs

Programs

  • Mathematica
    dircon[v_, w_] := Module[{lv = Length[v], lw = Length[w], fv, fw}, fv[n_] := If[n <= lv, v[[n]], 0]; fw[n_] := If[n <= lw, w[[n]], 0]; Table[ DirichletConvolve[fv[n], fw[n], n, m], {m, Min[lv, lw]}]];
    a[n_] := Module[{A, v, w, m}, If[n<1, 0, v = Table[Boole[k == 1], {k, n}]; For[k = 2, k <= n, k++, m = Length[IntegerDigits[n, k]] - 1; A = (1 + x)^(5^(k - 1)) + x*O[x]^m // Normal; w = Table[0, {n}]; For[i = 0, i <= m, i++, w[[k^i]] = Coefficient[A, x, i]]; v = dircon[v, w]]; v[[n]]]];
    Array[a, 26] (* after Jean-François Alcover in A007896 *)
Showing 1-7 of 7 results.