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

%I A274963 #14 Sep 08 2022 08:46:17
%S A274963 4,9,16,25,729,1681,3481,7921,10201,17161,552049,579121,1423249,
%T A274963 5812921,7091569,7447441,9066121,9765625,10374841,10569001,11895601,
%U A274963 22572001,38105929,43546801,46689889,52258441,75151561,82065481,86918329,90649441,94458961,94926049
%N A274963 Numbers n such that both sigma(n) and sigma(n) - 2 are primes.
%C A274963 Intersection of A249485 and A023194.
%C A274963 The next term, if it exists, must be greater than 10^8.
%C A274963 Each term is a square.
%C A274963 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
%H A274963 Chai Wah Wu, <a href="/A274963/b274963.txt">Table of n, a(n) for n = 1..10539</a>
%e A274963 729 is in the sequence because sigma(729) = 1093 and 1091 are both primes.
%o A274963 (Magma) [n: n in[1..10^7] | IsPrime(SumOfDivisors(n)) and IsPrime(SumOfDivisors(n)-2)]
%o A274963 (Python)
%o A274963 from sympy import isprime, divisor_sigma
%o A274963 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
%Y A274963 Cf. A000203, A023194, A249485, A274962.
%K A274963 nonn
%O A274963 1,1
%A A274963 _Jaroslav Krizek_, Jul 12 2016