A063900 Numbers k such that sum of proper divisors or aliquot parts of k^2 (excluding 1) is a square, or A048050(k^2) is a square.

866, 9271, 18167, 30887, 39959, 114607, 119279, 129911, 153631, 239111, 343207, 517591, 582583, 602159, 607340, 1202282, 1397863, 1729999, 1920647, 2533183, 2547119, 2558183, 5740127, 7122959, 9379871, 10218407, 10891103, 13549399

Offset: 1

Author

Jason Earls, Aug 29 2001

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100 (terms 1..55 from Harry J. Smith)
• Passawan Noppakaew and Prapanpong Pongsriiam, Product of Some Polynomials and Arithmetic Functions, J. Int. Seq. (2023) Vol. 26, Art. 23.9.1.

Crossrefs

Cf. A008847, A048050.

Programs

Mathematica

chowla[n_] := DivisorSigma[1, n] - n - 1; aQ[n_] := IntegerQ@Sqrt@chowla[n^2]; Select[Range[10^6], aQ] (* Amiram Eldar, Aug 30 2019 *)

PARI

s(n)=sigma(n)-n-1;
for(n=1,10^8, if(issquare(s(n^2)),print(n)))

PARI

s(n)=sigma(n) - n - 1
{ n=0; for (m=1, 10^9, if(issquare(s(m^2)), write("b063900.txt", n++, " ", m); if (n==55, break)) ) } \\ Harry J. Smith, Sep 02 2009

Extensions

a(19)-a(28) from Harry J. Smith, Sep 02 2009