A195268 Numbers whose sum of odd divisors is prime.

9, 18, 25, 36, 50, 72, 100, 144, 200, 288, 289, 400, 576, 578, 729, 800, 1152, 1156, 1458, 1600, 1681, 2304, 2312, 2401, 2916, 3200, 3362, 3481, 4608, 4624, 4802, 5041, 5832, 6400, 6724, 6962, 7921, 9216, 9248, 9604, 10082, 10201, 11664, 12800

Offset: 1

Author

Michel Lagneau, Sep 14 2011

Keywords

• nonn

Comments

Odd numbers k^2 such that sigma(k^2) is prime, times an arbitrary power of two. - Charles R Greathouse IV, Sep 14 2011

Examples

			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.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A028982.

Cf. A023194, A055638.

Programs

Maple

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:

Mathematica

Select[Range[13000], PrimeQ[DivisorSigma[1, #/2^IntegerExponent[#, 2]]] &] (* Amiram Eldar, Jul 31 2022 *)

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