A275250 Odd numbers n that divide the number of divisors of n!.

1, 27, 45, 105, 125, 135, 175, 189, 225, 231, 243, 297, 315, 351, 375, 385, 405, 441, 455, 495, 525, 539, 567, 585, 595, 605, 625, 637, 663, 675, 693, 715, 729, 735, 741, 765, 819, 825, 845, 847, 855, 875, 891, 935, 945, 969, 975, 1001, 1029, 1035, 1045, 1053, 1089

Offset: 1

Author

Altug Alkan, Jul 21 2016

Keywords

• nonn

Comments

Odd terms of A051178.

Examples

			The odd number 27 is a term because A000005(27!) = 2^9*3^3*7^2 is divisible by 27.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051178, A027423.

Programs

Maple

N:= 2000: # to get all terms <= N
P:= select(isprime, [2,seq(i,i=3..N,2)]):
d:= Vector(nops(P),1):
A:= 1:
for n from 2 to N do
  f:= ifactors(n)[2];
  for t in f do
    if member(t[1],P,'k') then
        d[k]:= d[k] + t[2]
    fi
  od:
  if n::odd and convert(d,`*`) mod n = 0 then A:= A, n fi;
od:
A; # Robert Israel, Aug 05 2016

Mathematica

A275250Q = OddQ[#] && Divisible[DivisorSigma[0, #!], #] &; Select[Range[500], A275250Q] (* JungHwan Min, Jul 29 2016 *)

PARI

isok(n) = (n % 2) && !(numdiv(n!) % n); \\ Michel Marcus, Jul 26 2016