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A248823 Number of integers k^5 that divide 1!*2!*3!*...*n!. 5
1, 1, 1, 2, 2, 6, 8, 10, 42, 64, 200, 432, 588, 1024, 3888, 6300, 21120, 33696, 52080, 114240, 328320, 816480, 3326400, 4435200, 6469632, 20616960, 57153600, 145411200, 258003900, 320973840, 791513856, 1634592960, 6403719168, 9967104000, 34939296000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Clark Kimberling and Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 400 terms from Clark Kimberling)

EXAMPLE

a(6) counts these integers k^5 that divide 24883200:  1, 32, 1024, 7776, 32768, 248832, these being k^5 for k = 1, 2, 3, 4, 6, 12.

MAPLE

b:= proc(n) option remember; add(i[2]*x^numtheory[pi](i[1]),

      i=ifactors(n)[2])+`if`(n=1, 0, b(n-1))

    end:

c:= proc(n) option remember; b(n)+`if`(n=1, 0, c(n-1)) end:

a:= n->(p->mul(iquo(coeff(p, x, i), 5)+1, i=1..degree(p)))(c(n)):

seq(a(n), n=1..30);  # Alois P. Heinz, Oct 16 2014

MATHEMATICA

z = 40; p[n_] := Product[k!, {k, 1, n}];

f[n_] := f[n] = FactorInteger[p[n]];

r[m_, x_] := r[m, 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]]}];

t[m_, n_] := Apply[Times, 1 + r[m, v[n]]/m]

m = 5; Table[t[m, n], {n, 1, z}] (* A248823 *)

CROSSREFS

Cf. A000178, A248784, A248821, A248822.

Sequence in context: A320247 A320248 A320067 * A284616 A136513 A214932

Adjacent sequences:  A248820 A248821 A248822 * A248824 A248825 A248826

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 15 2014

STATUS

approved

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Last modified March 20 09:35 EDT 2019. Contains 321345 sequences. (Running on oeis4.)