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 A318443 Numerators of the sequence whose Dirichlet convolution with itself yields A018804, Pillai's arithmetical function: Sum_{k=1..n} gcd(k, n). 3
 1, 3, 5, 23, 9, 15, 13, 91, 59, 27, 21, 115, 25, 39, 45, 1451, 33, 177, 37, 207, 65, 63, 45, 455, 179, 75, 353, 299, 57, 135, 61, 5797, 105, 99, 117, 1357, 73, 111, 125, 819, 81, 195, 85, 483, 531, 135, 93, 7255, 363, 537, 165, 575, 105, 1059, 189, 1183, 185, 171, 117, 1035, 121, 183, 767, 46355, 225, 315, 133, 759, 225, 351, 141, 5369 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Because A018804 gets only odd values on primes, 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) * (A018804(n) - Sum_{d|n, d>1, d 1. MATHEMATICA a18804[n_] := Sum[n EulerPhi[d]/d, {d, Divisors[n]}]; f[1] = 1; f[n_] := f[n] = 1/2 (a18804[n] - Sum[f[d] f[n/d], {d, Divisors[ n][[2 ;; -2]]}]); a[n_] := f[n] // Numerator; Array[a, 72] (* Jean-François Alcover, Sep 13 2018 *) PROG (PARI) up_to = 16384; A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804 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 15 06:46 EDT 2021. Contains 343909 sequences. (Running on oeis4.)