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

1,6

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

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

Sequence in context: A305945 A010855 A226757 * A238409 A040241 A278348

Adjacent sequences: A248761 A248762 A248763 * A248765 A248766 A248767

Keyword

nonn,easy

Author

Clark Kimberling, Oct 14 2014

Status

approved