A344268 -id:A344268 - cp's OEIS frontend

A344265 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(2^(k-1)).

1, 2, 4, 9, 16, 40, 64, 144, 262, 544, 1024, 2148, 4096, 8320, 16448, 33060, 65536, 131724, 262144, 525456, 1048832, 2099200, 4194304, 8393568, 16777336, 33562624, 67109892, 134234688, 268435456, 536906368, 1073741824, 2147550392, 4294971392, 8590065664, 17179870208

Offset: 1

Ilya Gutkovskiy, May 13 2021

nonn

Cf. A045778, A050368, A329800, A344266, A344267, A344268, A344269, A344270, A344271.

A344266 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(3^(k-1)).

Original entry on oeis.org

1, 3, 9, 30, 81, 270, 729, 2269, 6597, 19926, 59049, 178146, 531441, 1596510, 4783698, 14355900, 43046721, 129162141, 387420489, 1162322946, 3486790962, 10460530350, 31381059609, 94143737979, 282429539721, 847290203766, 2541865887462, 7625602289826, 22876792454961, 68630391912807

Offset: 1

Ilya Gutkovskiy, May 13 2021

nonn

Cf. A045778, A050368, A344247, A344265, A344267, A344268, A344269, A344270, A344271.

A344267 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(4^(k-1)).

Original entry on oeis.org

1, 4, 16, 70, 256, 1088, 4096, 16644, 65656, 263168, 1048576, 4199520, 16777216, 67125248, 268439552, 1073809761, 4294967296, 17180148192, 68719476736, 274878973440, 1099511693312, 4398050705408, 17592186044416, 70368761292864, 281474976743296, 1125899973951488, 4503599628419632

Offset: 1

Ilya Gutkovskiy, May 13 2021

nonn

Cf. A045778, A050368, A344248, A344265, A344266, A344268, A344269, A344270, A344271.

A344269 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(6^(k-1)).

Original entry on oeis.org

1, 6, 36, 231, 1296, 7992, 46656, 281252, 1680246, 10085472, 60466176, 362852028, 2176782336, 13060973952, 78364210752, 470186690667, 2821109907456, 16926669806148, 101559956668416, 609359800776048, 3656158441742592, 21936951003174912, 131621703842267136, 789730225242306480

Offset: 1

Ilya Gutkovskiy, May 13 2021

nonn

Cf. A045778, A050368, A344250, A344265, A344266, A344267, A344268, A344270, A344271.

A344270 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(7^(k-1)).

Original entry on oeis.org

1, 7, 49, 364, 2401, 17150, 117649, 825979, 5765977, 40370414, 282475249, 1977462228, 13841287201, 96889833950, 678223190498, 4747567340635, 33232930569601, 232630555172589, 1628413597910449, 11398895468722356, 79792266303376802, 558545866060610750, 3909821048582988049, 27368747353968794263

Offset: 1

Ilya Gutkovskiy, May 13 2021

nonn

Cf. A045778, A050368, A344251, A344265, A344266, A344267, A344268, A344269, A344271.

A344271 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(8^(k-1)).

Original entry on oeis.org

1, 8, 64, 540, 4096, 33280, 262144, 2101304, 16779232, 134250496, 1073741824, 8590231296, 68719476736, 549757911040, 4398046773248, 35184389011270, 281474976710656, 2251799950016256, 18014398509481984, 144115189151809536, 1152921504623624192, 9223372045444710400, 73786976294838206464

Offset: 1

Ilya Gutkovskiy, May 13 2021

nonn

Cf. A045778, A050368, A344252, A344265, A344266, A344267, A344268, A344269, A344270.

A344298 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(9^(k-1)).

Original entry on oeis.org

1, 9, 81, 765, 6561, 59778, 531441, 4789614, 43049961, 387479538, 3486784401, 31381653015, 282429536481, 2541870611298, 22876792986402, 205891175433096, 1853020188851841, 16677182091899187, 150094635296999121, 1350851721164795655, 12157665459099975522, 109418989162893418818

Offset: 1

Ilya Gutkovskiy, May 14 2021

nonn

Cf. A045778, A050368, A344253, A344265, A344266, A344267, A344268, A344269, A344270, A344271.

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)^(9^(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, 22] (* after Jean-François Alcover in A007896 *)

cp's OEIS Frontend

A344265 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(2^(k-1)).

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A344266 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(3^(k-1)).

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A344267 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(4^(k-1)).

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A344269 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(6^(k-1)).

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A344270 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(7^(k-1)).

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A344271 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(8^(k-1)).

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A344298 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(9^(k-1)).

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Programs

Mathematica