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A275250
Odd numbers n that divide the number of divisors of n!.
1
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
1,2
COMMENTS
Odd terms of A051178.
LINKS
EXAMPLE
The odd number 27 is a term because A000005(27!) = 2^9*3^3*7^2 is divisible by 27.
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 *)
PROG
(PARI) isok(n) = (n % 2) && !(numdiv(n!) % n); \\ Michel Marcus, Jul 26 2016
CROSSREFS
Sequence in context: A039325 A043148 A043928 * A223019 A059658 A241407
KEYWORD
nonn
AUTHOR
Altug Alkan, Jul 21 2016
STATUS
approved