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A195268 Numbers such that the sum of the odd divisors is prime. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Odd numbers n^2 such that sigma(n^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:

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.

Sequence in context: A034046 A069562 A072502 * A328252 A227279 A102042

Adjacent sequences:  A195265 A195266 A195267 * A195269 A195270 A195271

KEYWORD

nonn

AUTHOR

Michel Lagneau, Sep 14 2011

STATUS

approved

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Last modified December 5 10:45 EST 2019. Contains 329751 sequences. (Running on oeis4.)