OFFSET
1,6
COMMENTS
Every term divides all its successors.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = n!/A248766(n).
From Amiram Eldar, Sep 01 2024: (Start)
a(n) = A008835(n!).
a(n) = A248765(n)^4. (End)
EXAMPLE
a(6) = 16 because 16 divides 6! and if k > 2 then k^4 does not divide 6!.
MATHEMATICA
z = 40; f[n_] := f[n] = FactorInteger[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]]}];
p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
m = 4; Table[p[m, n], {n, 1, z}] (* A248764 *)
Table[p[m, n]^(1/m), {n, 1, z}] (* A248765 *)
Table[n!/p[m, n], {n, 1, z}] (* A248766 *)
f[p_, e_] := p^(4*Floor[e/4]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n!]; Array[a, 30] (* Amiram Eldar, Sep 01 2024 *)
PROG
(PARI) a(n) = {my(f = factor(n!)); prod(i = 1, #f~, f[i, 1]^(4*(f[i, 2]\4))); } \\ Amiram Eldar, Sep 01 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 14 2014
STATUS
approved