A248764 Greatest 4th power integer that divides n!

1, 1, 1, 1, 1, 16, 16, 16, 1296, 20736, 20736, 20736, 20736, 20736, 20736, 331776, 331776, 429981696, 429981696, 268738560000, 268738560000, 268738560000, 268738560000, 4299816960000, 4299816960000, 4299816960000, 348285173760000, 13379723235164160000

Offset: 1

Author

Clark Kimberling, Oct 14 2014

Keywords

• nonn
• easy

Comments

Every term divides all its successors.

Examples

			a(6) = 16 because 16 divides 6! and if k > 2 then k^4 does not divide 6!.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000142, A008835, A248762, A248765, A248766.

Programs

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 *)

PARI

a(n) = {my(f = factor(n!)); prod(i = 1, #f~, f[i, 1]^(4*(f[i, 2]\4)));} \\ Amiram Eldar, Sep 01 2024

Formula

a(n) = n!/A248766(n).

From Amiram Eldar, Sep 01 2024: (Start)

a(n) = A008835(n!).

a(n) = A248765(n)^4. (End)