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 A187087 Positive squares in the order of their appearance in A048050. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 9 19:10 EDT 2023. Contains 363183 sequences. (Running on oeis4.)