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 A317940 Numerators of sequence whose Dirichlet convolution with itself yields A046644. 5
 1, 1, 1, 7, 1, 1, 1, 9, 7, 1, 1, 7, 1, 1, 1, 427, 1, 7, 1, 7, 1, 1, 1, 9, 7, 1, 9, 7, 1, 1, 1, 471, 1, 1, 1, 49, 1, 1, 1, 9, 1, 1, 1, 7, 7, 1, 1, 427, 7, 7, 1, 7, 1, 9, 1, 9, 1, 1, 1, 7, 1, 1, 7, 4099, 1, 1, 1, 7, 1, 1, 1, 63, 1, 1, 7, 7, 1, 1, 1, 427, 427, 1, 1, 7, 1, 1, 1, 9, 1, 7, 1, 7, 1, 1, 1, 471, 1, 7, 7, 49, 1, 1, 1, 9, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Multiplicative because A046644 is. No negative terms among the first 2^20 terms. Is the sequence nonnegative? LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A046644(n) - Sum_{d|n, d>1, d 1. PROG (PARI) up_to = 65537; DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d>=1, s+=n); s; }; A046644(n) = factorback(apply(e -> 2^A005187(e), factor(n)[, 2])); v317940aux = DirSqrt(vector(up_to, n, A046644(n))); A317940(n) = numerator(v317940aux[n]); CROSSREFS Cf. A005187, A046644, A317934 (denominators), A317941. Sequence in context: A365332 A367483 A348281 * A318674 A284118 A165725 Adjacent sequences: A317937 A317938 A317939 * A317941 A317942 A317943 KEYWORD nonn,frac,mult AUTHOR Antti Karttunen, Aug 14 2018 STATUS approved

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Last modified May 25 11:12 EDT 2024. Contains 372788 sequences. (Running on oeis4.)