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A275250 Odd numbers n that divide the number of divisors of n!. 1

%I

%S 1,27,45,105,125,135,175,189,225,231,243,297,315,351,375,385,405,441,

%T 455,495,525,539,567,585,595,605,625,637,663,675,693,715,729,735,741,

%U 765,819,825,845,847,855,875,891,935,945,969,975,1001,1029,1035,1045,1053,1089

%N Odd numbers n that divide the number of divisors of n!.

%C Odd terms of A051178.

%H Robert Israel, <a href="/A275250/b275250.txt">Table of n, a(n) for n = 1..10000</a>

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

%p N:= 2000: # to get all terms <= N

%p P:= select(isprime, [2,seq(i,i=3..N,2)]):

%p d:= Vector(nops(P),1):

%p A:= 1:

%p for n from 2 to N do

%p f:= ifactors(n)[2];

%p for t in f do

%p if member(t[1],P,'k') then

%p d[k]:= d[k] + t[2]

%p fi

%p od:

%p if n::odd and convert(d,`*`) mod n = 0 then A:= A, n fi;

%p od:

%p A; # _Robert Israel_, Aug 05 2016

%t A275250Q = OddQ[#] && Divisible[DivisorSigma[0, #!], #] &; Select[Range[500], A275250Q] (* _JungHwan Min_, Jul 29 2016 *)

%o (PARI) isok(n) = (n % 2) && !(numdiv(n!) % n); \\ _Michel Marcus_, Jul 26 2016

%Y Cf. A051178, A027423.

%K nonn

%O 1,2

%A _Altug Alkan_, Jul 21 2016

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Last modified May 21 15:32 EDT 2019. Contains 323444 sequences. (Running on oeis4.)