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 A248783 Number of integers k^6 that divide n!. 1
 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 6, 8, 8, 8, 8, 8, 16, 16, 24, 30, 30, 30, 30, 36, 36, 36, 36, 36, 36, 36, 48, 56, 56, 112, 112, 112, 112, 128, 128, 128, 128, 192, 192, 216, 216, 270, 270, 270, 270, 300, 300, 300, 300, 300, 360, 396, 396 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 EXAMPLE a(16) counts these divisors of 16!: 1^6, 2^6, 2^12, 3^6, 6^6, 12^6. MATHEMATICA z = 130; m = 6; f[n_] := f[n] = FactorInteger[n!]; r[x_] := r[x] = m*Floor[x/m] u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}]; v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}]; a[n_] := Apply[Times, 1 + r[v[n]]/m] t = Table[a[n], {n, 1, z}] (* A248783 *) PROG (PARI) a(n)=c=0; d=divisors(n!); for(i=1, #d, if(ispower(d[i])&&ispower(d[i])%6==0, c++)); c+1 n=1; while(n<50, print1(a(n), ", "); n++) \\ Derek Orr, Oct 20 2014 CROSSREFS Cf. A000142, A055993, A248780, A248781, A248782, A248771. Sequence in context: A105267 A280263 A008838 * A244462 A063790 A334510 Adjacent sequences: A248780 A248781 A248782 * A248784 A248785 A248786 KEYWORD nonn,easy AUTHOR Clark Kimberling, Oct 15 2014 STATUS approved

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Last modified March 4 14:35 EST 2024. Contains 370532 sequences. (Running on oeis4.)