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%I #23 Aug 04 2022 05:55:07
%S 9,18,25,36,50,72,100,144,200,288,289,400,576,578,729,800,1152,1156,
%T 1458,1600,1681,2304,2312,2401,2916,3200,3362,3481,4608,4624,4802,
%U 5041,5832,6400,6724,6962,7921,9216,9248,9604,10082,10201,11664,12800
%N Numbers whose sum of odd divisors is prime.
%C Odd numbers k^2 such that sigma(k^2) is prime, times an arbitrary power of two. - _Charles R Greathouse IV_, Sep 14 2011
%H Charles R Greathouse IV, <a href="/A195268/b195268.txt">Table of n, a(n) for n = 1..10000</a>
%e The divisors of 2312 are { 1, 2, 4, 8, 17, 34, 68, 136, 289, 578, 1156, 2312 }, and the sum of the odd divisors 1 + 17 + 289 = 307 is prime. Hence 2312 = 2*34^2 is in the sequence.
%p with(numtheory):for n from 1 to 20000 do:x:=divisors(n):n1:=nops(x):s:=0:for m from 1 to n1 do:if irem(x[m],2)=1 then s:=s+x[m]:fi:od:if type(s,prime)=true then printf(`%d, `,n): else fi:od:
%t Select[Range[13000], PrimeQ[DivisorSigma[1, #/2^IntegerExponent[#, 2]]] &] (* _Amiram Eldar_, Jul 31 2022 *)
%o (PARI) list(lim)=my(v=List(),t);forstep(k=3,sqrt(lim),2,if(isprime(sigma(t=k^2)),listput(v,t);while((t<<=1)<=lim,listput(v,t)))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Sep 14 2011
%Y Subsequence of A028982.
%Y Cf. A023194, A055638.
%K nonn
%O 1,1
%A _Michel Lagneau_, Sep 14 2011
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