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
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
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
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
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
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
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 *)
Showing 1-7 of 7 results.