A274963 Numbers n such that both sigma(n) and sigma(n) - 2 are primes.

4, 9, 16, 25, 729, 1681, 3481, 7921, 10201, 17161, 552049, 579121, 1423249, 5812921, 7091569, 7447441, 9066121, 9765625, 10374841, 10569001, 11895601, 22572001, 38105929, 43546801, 46689889, 52258441, 75151561, 82065481, 86918329, 90649441, 94458961, 94926049

Offset: 1

Author

Jaroslav Krizek, Jul 12 2016

Keywords

• nonn

Comments

Intersection of A249485 and A023194.

The next term, if it exists, must be greater than 10^8.

Each term is a square.

Most of the terms seem to be of the form p^2 for some prime p. Out of the first 10539 terms, 6 of them are not of the form p^2. - Chai Wah Wu, Jul 13 2016

Examples

			729 is in the sequence because sigma(729) = 1093 and 1091 are both primes.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10539

Crossrefs

Cf. A000203, A023194, A249485, A274962.

Programs

Magma

[n: n in[1..10^7] | IsPrime(SumOfDivisors(n)) and IsPrime(SumOfDivisors(n)-2)]

Python

from sympy import isprime, divisor_sigma
A274963_list = [n for n, s in ((d**2, divisor_sigma(d**2)) for d in range(1,10**3)) if isprime(s) and isprime(s-2)] # Chai Wah Wu, Jul 13 2016