cp's OEIS Frontend

A201880 Numbers n such that sigma_2(n) - n^2 is prime.

%I A201880 #17 Aug 16 2019 12:31:48
%S A201880 4,18,21,33,39,72,93,99,100,159,171,177,189,207,213,231,245,249,261,
%T A201880 275,291,297,303,333,338,357,369,381,399,400,453,471,475,477,484,495,
%U A201880 537,539,543,561,609,633,648,657,669,681,711,717,783,801,833,861,909,927
%N A201880 Numbers n such that sigma_2(n) - n^2 is prime.
%C A201880 Numbers n such that sum of the squares of the proper (or aliquot) divisors of n is a prime number.
%H A201880 Amiram Eldar, <a href="/A201880/b201880.txt">Table of n, a(n) for n = 1..10000</a>
%F A201880 {n: A067558(n) in A000040} - _R. J. Mathar_, Dec 07 2011
%e A201880 a(3)=21 because the aliquot divisors of 21 are 1, 3, 7, the sum of whose squares is 1^2 + 3^2 + 7^2 = 59, prime.
%p A201880 A067558 := proc(n)
%p A201880     numtheory[sigma][2](n)-n^2 ;
%p A201880 end proc:
%p A201880 isA201880 := proc(n)
%p A201880     isprime(A067558(n)) ;
%p A201880 end proc:
%p A201880 for n from 1 to 1000 do
%p A201880     if isA201880(n) then
%p A201880         printf("%d,",n);
%p A201880     end if;
%p A201880 end do: # _R. J. Mathar_, Dec 07 2011
%t A201880 Select[Range[400], PrimeQ[DivisorSigma[2, #]-#^2]&]
%o A201880 (PARI) is(n)=isprime(sigma(n,2)-n^2) \\ _Charles R Greathouse IV_, Dec 06 2011
%Y A201880 Cf. A001157, A037020, A067558.
%K A201880 nonn
%O A201880 1,1
%A A201880 _Michel Lagneau_, Dec 06 2011