A274795 Least k such that d(k*n) = d(n!) (d = A000005).

1, 1, 2, 6, 24, 120, 720, 3465, 18480, 194040, 2293200, 19219200, 301593600, 1163962800, 6518191680, 20078358300, 548021073600, 42643458457600, 1090774779494400, 15198128594288640, 136285012131840000, 55135902013920000, 1951331488666560000, 9736473836722913280000

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Example

a(8) = 3465 because A000005(3465*8) = A000005(8!).

Mathematica

dec[v_, w_] := If[v == 1, Sow@w, dec[v/#, Append[w, #]] & /@ Select[Rest@ Divisors@ v, # <= w[[-1]] &]]; mul[n_] := Reap[dec[n/#, {#}] & /@ Rest@ Divisors@n][[2, 1]]; ev[e_] := Times @@ (Prime[ Range@ Length@ e]^e); a[n_] := If[n == 1, 1, Min[ev /@ (mul[ DivisorSigma[0, n!]] - 1)]/n]; Array[a, 24] (* Giovanni Resta, Jul 29 2016 *)

Crossrefs

Cf. A000005, A027423.

Sequence in context: A189853 A189857 A189860 * A174702 A173846 A154654

Adjacent sequences: A274792 A274793 A274794 * A274796 A274797 A274798

Keyword

nonn

Author

Altug Alkan, Jul 29 2016

Extensions

a(12)-a(24) from Giovanni Resta, Jul 29 2016

Status

approved