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A244342 a(n) = phi(n)*h(n) where phi() is the Euler totient function, A000010, and h() is A092089. 2
1, 2, 6, 8, 12, 12, 18, 32, 30, 24, 30, 48, 36, 36, 72, 96, 48, 60, 54, 96, 108, 60, 66, 192, 100, 72, 126, 144, 84, 144, 90, 256, 180, 96, 216, 240, 108, 108, 216, 384, 120, 216, 126, 240, 360, 132, 138, 576, 210, 200, 288, 288, 156, 252, 360, 576, 324, 168 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) = Sum_{k=1..n} gcd(k^2-1, n) for those k that are coprime to n (see proof in link).
Multiplicative because both A000010 and A092089 are. - Andrew Howroyd, Jul 26 2018
LINKS
László Tóth, Menon's identity and arithmetical sums representing functions of several variables, Rend. Sem. Mat. Univ. Politec. Torino, 69 (2011), 97-110 (see (36) in Corollary 15, p. 108); also on arXiv, arXiv:1103.5861 [math.NT], 2011.
MAPLE
A244342:= proc(n) add(`if`(igcd(k, n)=1, igcd(k^2-1, n), 0), k=1..n) end proc;
seq(A244342(i), i=1..1000); # Robert Israel, Jul 06 2014
MATHEMATICA
h[n_] := Product[{p, e} = pe; Which[OddQ[p], 2 e + 1, p == 2 && e == 1, 2, True, 4 (e - 1)], {pe, FactorInteger[n]}]; h[1] = 1;
a[n_] := EulerPhi[n] h[n];
Array[a, 100] (* Jean-François Alcover, Apr 08 2020 *)
PROG
(PARI) a(n) = sum(j=1, n, gcd(j^2-1, n)*(gcd(j, n)==1));
CROSSREFS
Sequence in context: A130205 A054067 A250190 * A064212 A056906 A257056
KEYWORD
nonn,mult
AUTHOR
Michel Marcus, Jun 26 2014
STATUS
approved

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Last modified July 13 02:40 EDT 2024. Contains 374261 sequences. (Running on oeis4.)