A187087 Positive squares in the order of their appearance in A048050.

9, 16, 49, 25, 16, 49, 64, 121, 36, 81, 64, 169, 36, 225, 100, 225, 64, 36, 441, 36, 169, 361, 225, 144, 441, 441, 144, 256, 400, 196, 64, 441, 144, 361, 64, 400, 441, 729, 961, 64, 196, 144, 729, 100, 841, 729, 400, 256, 1225, 100, 729, 1225, 961, 900, 841

Offset: 1

Author

Zak Seidov, Mar 04 2011

Keywords

• nonn

Comments

Corresponding values of n are in A187086. A048050 is Chowla's function: sum of divisors of n except 1 and n.

By the Goldbach conjecture, every even square appears; take two odd primes p and q such that p+q = k^2, then Chowla function of p*q is k^2. It appears that 17^2 is the first odd square not in A048050.

Links

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

Crossrefs

Cf. A048050, A187086.

Programs

Magma

A048050:=func< n | n eq 1 or IsPrime(n) select 0 else &+[ a: a in Divisors(n) | a ne 1 and a ne n ] >; [ a: n in [1..2500] | a gt 0 and IsSquare(a) where a is A048050(n) ]; // Klaus Brockhaus, Mar 04 2011

Mathematica

chowla[n_] := DivisorSigma[1, n] - n - 1; s = {}; Do[c = chowla[n]; If[c > 0 && IntegerQ@Sqrt[c], AppendTo[s, c]], {n, 1, 10^3}]; s (* Amiram Eldar, Aug 28 2019 *)

PARI

{for(n=1,2000,spf=sumdiv(n,x,x)-1-n;if(spf>0&&issquare(spf),print1(spf",")))}