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 A343490 a(n) = Sum_{k=1..n} 4^(gcd(k, n) - 1). 2
 1, 5, 18, 70, 260, 1050, 4102, 16460, 65574, 262420, 1048586, 4195500, 16777228, 67112990, 268436040, 1073758360, 4294967312, 17179936830, 68719476754, 274878169880, 1099511636076, 4398047559730, 17592186044438, 70368748407000, 281474976711700, 1125899923619900 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Robert Israel, Table of n, a(n) for n = 1..1660 FORMULA a(n) = Sum_{d|n} phi(n/d)*4^(d - 1) = A054611(n)/4. G.f.: Sum_{k>=1} phi(k) * x^k / (1 - 4*x^k). MAPLE N:= 30: # for a(1)..a(N) G:= add(numtheory:-phi(k)*x^k/(1-4*x^k), k=1..N): S:= series(G, x, N+1): seq(coeff(S, x, j), j=1..N); # Robert Israel, Sep 11 2023 MATHEMATICA a[n_] := Sum[4^(GCD[k, n] - 1), {k, 1, n}]; Array[a, 26] (* Amiram Eldar, Apr 17 2021 *) PROG (PARI) a(n) = sum(k=1, n, 4^(gcd(k, n)-1)); (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*4^(d-1)); (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-4*x^k))) CROSSREFS Column 4 of A343489. Cf. A000010, A054611. Sequence in context: A164051 A134764 A188177 * A302077 A322773 A145780 Adjacent sequences: A343487 A343488 A343489 * A343491 A343492 A343493 KEYWORD nonn AUTHOR Seiichi Manyama, Apr 17 2021 STATUS approved

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Last modified September 29 14:55 EDT 2023. Contains 365772 sequences. (Running on oeis4.)