A038688 Squares that are the sum of the divisors of some number.

1, 4, 36, 121, 144, 256, 324, 400, 576, 784, 900, 961, 1024, 1296, 1600, 1764, 1936, 2304, 2704, 2916, 3136, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5776, 6084, 6400, 7056, 7744, 8100, 9216, 9604, 10000, 10404, 10816, 11664, 12544, 12996, 14400

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: Inversion of Multiplicative Functions (invphi.gp).

Crossrefs

Intersection of A000290 and A002191.

Cf. A000203, A006532, A228061.

Programs

Mathematica

nn = 14400; t = Select[Union[DivisorSigma[1, Range[nn]]], IntegerQ[Sqrt[#]] &]; t = Select[t, # <= nn &] (* T. D. Noe, Sep 04 2013 *)

PARI

lista(kmax) = for(k = 1, kmax, if(invsigmaNum(k^2) > 0, print1(k^2, ", "))); \\ Amiram Eldar, Aug 12 2024, using Max Alekseyev's invphi.gp

Formula

a(n) = A228061(n)^2. - Amiram Eldar, Aug 12 2024