cp's OEIS Frontend

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

%I A275250 #17 Aug 06 2016 09:38:47
%S A275250 1,27,45,105,125,135,175,189,225,231,243,297,315,351,375,385,405,441,
%T A275250 455,495,525,539,567,585,595,605,625,637,663,675,693,715,729,735,741,
%U A275250 765,819,825,845,847,855,875,891,935,945,969,975,1001,1029,1035,1045,1053,1089
%N A275250 Odd numbers n that divide the number of divisors of n!.
%C A275250 Odd terms of A051178.
%H A275250 Robert Israel, <a href="/A275250/b275250.txt">Table of n, a(n) for n = 1..10000</a>
%e A275250 The odd number 27 is a term because A000005(27!) = 2^9*3^3*7^2 is divisible by 27.
%p A275250 N:= 2000: # to get all terms <= N
%p A275250 P:= select(isprime, [2,seq(i,i=3..N,2)]):
%p A275250 d:= Vector(nops(P),1):
%p A275250 A:= 1:
%p A275250 for n from 2 to N do
%p A275250   f:= ifactors(n)[2];
%p A275250   for t in f do
%p A275250     if member(t[1],P,'k') then
%p A275250         d[k]:= d[k] + t[2]
%p A275250     fi
%p A275250   od:
%p A275250   if n::odd and convert(d,`*`) mod n = 0 then A:= A, n fi;
%p A275250 od:
%p A275250 A; # _Robert Israel_, Aug 05 2016
%t A275250 A275250Q = OddQ[#] && Divisible[DivisorSigma[0, #!], #] &; Select[Range[500], A275250Q] (* _JungHwan Min_, Jul 29 2016 *)
%o A275250 (PARI) isok(n) = (n % 2) && !(numdiv(n!) % n); \\ _Michel Marcus_, Jul 26 2016
%Y A275250 Cf. A051178, A027423.
%K A275250 nonn
%O A275250 1,2
%A A275250 _Altug Alkan_, Jul 21 2016