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

4, 18, 21, 33, 39, 72, 93, 99, 100, 159, 171, 177, 189, 207, 213, 231, 245, 249, 261, 275, 291, 297, 303, 333, 338, 357, 369, 381, 399, 400, 453, 471, 475, 477, 484, 495, 537, 539, 543, 561, 609, 633, 648, 657, 669, 681, 711, 717, 783, 801, 833, 861, 909, 927

Offset: 1

Author

Michel Lagneau, Dec 06 2011

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A001157, A037020, A067558.

Programs

Maple

A067558 := proc(n)
    numtheory[sigma][2](n)-n^2 ;
end proc:
isA201880 := proc(n)
    isprime(A067558(n)) ;
end proc:
for n from 1 to 1000 do
    if isA201880(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Dec 07 2011

Mathematica

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

PARI

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

Formula

{n: A067558(n) in A000040} - R. J. Mathar, Dec 07 2011