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Prime powers p^m for which sigma(p^2m) is not prime.
2

%I #16 Aug 18 2019 04:31:38

%S 1,7,9,11,13,16,19,23,25,29,31,32,37,43,47,53,61,67,73,79,81,83,97,

%T 103,107,109,113,121,127,128,137,139,149,151,157,163,179,181,191,193,

%U 197,199,211,223,227,229,233,239,241,243,251,257,263,269,271,277,281,283,307,311,313,317,331

%N Prime powers p^m for which sigma(p^2m) is not prime.

%C sigma(x) cannot be prime unless x is a square of a prime power, x = p^2m, cf. A055638 and A023194. This sequence lists the complement: prime powers whose square does not have a prime sum of divisors.

%C Although generally 1 is not considered a prime power, it seemed logical for various good reasons to include the initial term a(1)=1.

%H Amiram Eldar, <a href="/A248963/b248963.txt">Table of n, a(n) for n = 1..10000</a>

%F A248963 = A000961 \ A055638, i.e., the complement of A055638 in A000961.

%o (PARI) for(n=1,999,isprimepower(n)||next;isprime(sigma(n^2))||print1((n)","))

%Y Cf. A000961, A055638, A023194, A023195, A062700.

%K nonn

%O 1,2

%A _M. F. Hasler_, Oct 18 2014