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

1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 61, 67, 70, 71, 73, 79, 83, 89, 97, 101, 102, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257

Offset: 1

Author

Michel Lagneau, Dec 06 2011

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A001065, A001157, A073040.

Programs

Maple

A067558 := proc(n)
    numtheory[sigma][2](n)-n^2 ;
end proc:
isA201879 := proc(n)
    issqr(A067558(n)) ;
end proc:
for n from 1 to 300 do
    if isA201879(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Dec 07 2011

Mathematica

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

PARI

is(n)=issquare(sigma(n,2)-n^2) \\ Charles R Greathouse IV, Dec 06 2011

Formula

{n: A067558(n) in A000290}. - R. J. Mathar, Dec 07 2011