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
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
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
-
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 *)
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
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
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
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
-
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 *)
Showing 1-7 of 7 results.