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

1,1

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

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A000203, A023194, A249485, A274962.

Sequence in context: A133900 A143480 A230365 * A353387 A050461 A189835

Adjacent sequences: A274960 A274961 A274962 * A274964 A274965 A274966

Keyword

nonn

Author

Jaroslav Krizek, Jul 12 2016

Status

approved