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 A318444 Numerators of the sequence whose Dirichlet convolution with itself yields A057660(n) = Sum_{k=1..n} n/gcd(n,k). 2
 1, 3, 7, 35, 21, 21, 43, 239, 195, 63, 111, 245, 157, 129, 147, 6851, 273, 585, 343, 735, 301, 333, 507, 1673, 1643, 471, 3011, 1505, 813, 441, 931, 50141, 777, 819, 903, 6825, 1333, 1029, 1099, 5019, 1641, 903, 1807, 3885, 4095, 1521, 2163, 47957, 6555, 4929, 1911, 5495, 2757, 9033, 2331, 10277, 2401, 2439, 3423 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Because A057660 contains only odd values, A046644 gives the sequence of denominators. Because both of those sequences are multiplicative, this is also. LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A057660(n) - Sum_{d|n, d>1, d 1. MATHEMATICA a57660[n_] := DivisorSigma[2, n^2]/DivisorSigma[1, n^2]; f[1] = 1; f[n_] := f[n] = 1/2 (a57660[n] - Sum[f[d]*f[n/d], {d, Divisors[ n][[2 ;; -2]]}]); Table[f[n] // Numerator, {n, 1, 60}] (* Jean-François Alcover, Sep 13 2018 *) PROG (PARI) up_to = 16384; A057660(n) = sumdivmult(n, d, eulerphi(d)*d); \\ From A057660 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

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)