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

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%I A187087 #17 Sep 08 2022 08:45:56
%S A187087 9,16,49,25,16,49,64,121,36,81,64,169,36,225,100,225,64,36,441,36,169,
%T A187087 361,225,144,441,441,144,256,400,196,64,441,144,361,64,400,441,729,
%U A187087 961,64,196,144,729,100,841,729,400,256,1225,100,729,1225,961,900,841
%N A187087 Positive squares in the order of their appearance in A048050.
%C A187087 Corresponding values of n are in A187086. A048050 is Chowla's function: sum of divisors of n except 1 and n.
%C A187087 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.
%H A187087 Amiram Eldar, <a href="/A187087/b187087.txt">Table of n, a(n) for n = 1..10000</a>
%t A187087 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 *)
%o A187087 (PARI) {for(n=1,2000,spf=sumdiv(n,x,x)-1-n;if(spf>0&&issquare(spf),print1(spf",")))}
%o A187087 (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
%Y A187087 Cf. A048050, A187086.
%K A187087 nonn
%O A187087 1,1
%A A187087 _Zak Seidov_, Mar 04 2011