A201879 - OEIS

%I #18 Aug 14 2019 08:27:37

%S 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 79,83,89,97,101,102,103,107,109,113,127,131,137,139,149,151,157,163,

%U 167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257

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

%C Numbers n such that sum of the square of proper (or aliquot) divisors of n is a square.

%C 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 Amiram Eldar, <a href="/A201879/b201879.txt">Table of n, a(n) for n = 1..10000</a>

%F {n: A067558(n) in A000290}. - _R. J. Mathar_, Dec 07 2011

%e 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 A067558 := proc(n)

%p     numtheory[sigma][2](n)-n^2 ;

%p end proc:

%p isA201879 := proc(n)

%p     issqr(A067558(n)) ;

%p end proc:

%p for n from 1 to 300 do

%p     if isA201879(n) then

%p         printf("%d,",n);

%p     end if;

%p end do: # _R. J. Mathar_, Dec 07 2011

%t Select[Range[400], IntegerQ[Sqrt[DivisorSigma[2, #]-#^2]]&]

%o (PARI) is(n)=issquare(sigma(n,2)-n^2) \\ _Charles R Greathouse IV_, Dec 06 2011

%Y Cf. A000290, A001065, A001157, A073040.

%K nonn

%O 1,2

%A _Michel Lagneau_, Dec 06 2011