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

1,1

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Subsequence of A028982.

Cf. A023194, A055638.

Sequence in context: A034046 A069562 A072502 * A371083 A328252 A227279

Adjacent sequences: A195265 A195266 A195267 * A195269 A195270 A195271

Keyword

nonn

Author

Michel Lagneau, Sep 14 2011

Status

approved