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

1,1

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

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 *)

Prog

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

Crossrefs

Cf. A048050, A187086.

Sequence in context: A067956 A270757 A203595 * A072861 A183371 A225528

Adjacent sequences: A187084 A187085 A187086 * A187088 A187089 A187090

Keyword

nonn

Author

Zak Seidov, Mar 04 2011

Status

approved