The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A248764

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A248764

Greatest 4th power integer that divides n!
(history; published version)

#10 by Michael De Vlieger at Sun Sep 01 09:37:35 EDT 2024

STATUS

reviewed

approved

#9 by Joerg Arndt at Sun Sep 01 02:40:36 EDT 2024

STATUS

proposed

reviewed

#8 by Amiram Eldar at Sun Sep 01 02:28:50 EDT 2024

STATUS

editing

proposed

#7 by Amiram Eldar at Sun Sep 01 02:18:55 EDT 2024

FORMULA

From Amiram Eldar, Sep 01 2024: (Start)

a(n) = A008835(n!).

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

MATHEMATICA

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, A248762, A000142.

STATUS

approved

editing

#6 by Jon E. Schoenfield at Sat Mar 14 10:09:59 EDT 2015

STATUS

editing

approved

#5 by Jon E. Schoenfield at Sat Mar 14 10:09:58 EDT 2015

NAME

Greatest 4-th 4th power integer that divides n!

STATUS

approved

editing

#4 by N. J. A. Sloane at Sun Oct 19 16:24:54 EDT 2014

STATUS

proposed

approved

#3 by Clark Kimberling at Sun Oct 19 15:30:02 EDT 2014

STATUS

editing

proposed

#2 by Clark Kimberling at Tue Oct 14 14:14:06 EDT 2014

NAME

allocated for Clark KimberlingGreatest 4-th power integer that divides n!

DATA

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, <a href="/A248764/b248764.txt">Table of n, a(n) for n = 1..1000</a>

FORMULA

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

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 *)

CROSSREFS

Cf. A248765, A248766, A248762, A000142.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, Oct 14 2014

STATUS

approved

editing

#1 by Clark Kimberling at Mon Oct 13 21:01:59 EDT 2014

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved