A187087 - OEIS

%I #17 Sep 08 2022 08:45:56

%S 9,16,49,25,16,49,64,121,36,81,64,169,36,225,100,225,64,36,441,36,169,

%T 361,225,144,441,441,144,256,400,196,64,441,144,361,64,400,441,729,

%U 961,64,196,144,729,100,841,729,400,256,1225,100,729,1225,961,900,841

%N Positive squares in the order of their appearance in A048050.

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

%C 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 Amiram Eldar, <a href="/A187087/b187087.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (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 Cf. A048050, A187086.

%K nonn

%O 1,1

%A _Zak Seidov_, Mar 04 2011