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A201879 Numbers n such that sigma_2(n) - n^2 is a square.

%I A201879 #18 Aug 14 2019 08:27:37
%S A201879 1,2,3,5,7,11,13,17,19,23,29,30,31,37,41,43,47,53,59,61,67,70,71,73,
%T A201879 79,83,89,97,101,102,103,107,109,113,127,131,137,139,149,151,157,163,
%U A201879 167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257
%N A201879 Numbers n such that sigma_2(n) - n^2 is a square.
%C A201879 Numbers n such that sum of the square of proper (or aliquot) divisors of n is a square.
%C A201879 All primes are in this sequence. Nonprimes in the sequence are 1, 30, 70, 102, 282, 286, 646, 730, 920, 1242, ...  - _Charles R Greathouse IV_, Dec 06 2011
%H A201879 Amiram Eldar, <a href="/A201879/b201879.txt">Table of n, a(n) for n = 1..10000</a>
%F A201879 {n: A067558(n) in A000290}. - _R. J. Mathar_, Dec 07 2011
%e A201879 a(12)=30 because the aliquot divisors of 30 are  1, 2, 3, 5, 6, 10, 15, the sum of whose squares is 1^2 + 2^2 + 3^2 + 5^2 + 6^2 + 10^2 + 15^2 = 400 = 20^2.
%p A201879 A067558 := proc(n)
%p A201879     numtheory[sigma][2](n)-n^2 ;
%p A201879 end proc:
%p A201879 isA201879 := proc(n)
%p A201879     issqr(A067558(n)) ;
%p A201879 end proc:
%p A201879 for n from 1 to 300 do
%p A201879     if isA201879(n) then
%p A201879         printf("%d,",n);
%p A201879     end if;
%p A201879 end do: # _R. J. Mathar_, Dec 07 2011
%t A201879 Select[Range[400], IntegerQ[Sqrt[DivisorSigma[2, #]-#^2]]&]
%o A201879 (PARI) is(n)=issquare(sigma(n,2)-n^2) \\ _Charles R Greathouse IV_, Dec 06 2011
%Y A201879 Cf. A000290, A001065, A001157, A073040.
%K A201879 nonn
%O A201879 1,2
%A A201879 _Michel Lagneau_, Dec 06 2011