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A065405
Composite numbers k such that the sum of the divisors of k^2 is a prime.
9
4, 8, 27, 49, 64, 125, 169, 256, 289, 512, 529, 729, 841, 1849, 2197, 3125, 4913, 5329, 6241, 6889, 15625, 16129, 29791, 32768, 37249, 51529, 57121, 69169, 76729, 113569, 117649, 128881, 139129, 157609, 192721, 208849, 226981, 229441, 253009
OFFSET
1,1
COMMENTS
All these composite numbers k should be prime powers because if k=a*b with gcd(a,b)=1, then sigma(aabb) = sigma(aa)*sigma(bb) cannot be a prime; 46 of the 236 prime powers below 1000000 are here.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..500 (terms 1..70 from Harry J. Smith)
FORMULA
sigma(a(n)^2) = sigma(A065404(n)) = A065403(n) is prime.
MATHEMATICA
Select[ Range[3 10^5], ! PrimeQ[ # ] && PrimeQ[ DivisorSigma[1, #^2]] & ]
PROG
(PARI) { n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), write("b065405.txt", n++, " ", m); if (n==70, return)) ) } \\ Harry J. Smith, Oct 18 2009
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 06 2001
STATUS
approved