A228567 Primes expressible as sigma(sigma(n)) - sigma(n), in order of their occurrence.

3, 7, 17, 31, 31, 41, 23, 73, 127, 73, 89, 127, 463, 523, 241, 523, 157, 241, 523, 463, 211, 257, 131, 983, 379, 1153, 311, 1153, 83, 983, 521, 4339, 4339, 113, 8893, 4339, 4339, 1093, 4339, 769, 2851, 8893, 4339, 1429, 1097, 4339, 1093, 4339, 8893, 4339, 8893

Offset: 1

Author

K. D. Bajpai, Nov 10 2013

Keywords

• nonn

Examples

			a(9)= 127: sigma(sigma(93))-sigma(93)= 255-128= 127, which is prime.
a(11)= 89: sigma(sigma(98))-sigma(98)= 260-171= 89, which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..2200

Crossrefs

Cf. A000203 (sigma(n): sum of divisors of n).

Cf. A019279 (superperfect numbers: sigma(sigma(n))=2n).

Cf. A033632 (numbers n: sigma(n)is prime).

Cf. A051027 (sigma(sigma(n))).

Programs

Maple

with(numtheory):KD := proc() local a; a:= sigma(sigma(n))-sigma(n);if isprime(a) then RETURN (a); fi; end: seq(KD(),n=1..5000);