OFFSET
1,2
COMMENTS
The sum of aliquot divisors of prime numbers is 1.
If a^2 is an odd square for which a^2-1 = p + q with p,q primes, then p*q is a term. If m = 2^k-1 is a Mersenne prime then m*(2^k) (twice an even perfect number) is a term. If b = 2^j is a square and b-7 = 3s is a semiprime then 4s is a term. - Metin Sariyar, Apr 02 2020
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3)=15; aliquot divisors are 1,3,5; sum of aliquot divisors = 9 and 3^2=9.
MAPLE
a := []; for n from 1 to 2000 do if sigma(n) <> n+1 and issqr(sigma(n)-n) then a := [op(a), n]; fi; od: a;
MATHEMATICA
nn=1400; Select[Complement[Range[nn], Prime[Range[PrimePi[nn]]]], IntegerQ[ Sqrt[DivisorSigma[1, #]-#]]&] (* Harvey P. Dale, Apr 25 2011 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved