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A274963
Numbers n such that both sigma(n) and sigma(n) - 2 are primes.
3
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
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jul 12 2016
STATUS
approved