A343467 - OEIS

A343467

a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-5)^d.

5, -10, 45, -160, 629, -2590, 11165, -48910, 217045, -976258, 4438925, -20346440, 93900245, -435959830, 2034505661, -9536767660, 44878791365, -211927519090, 1003867701485, -4768372070128, 22706531350485, -108372079190350, 518301258916445, -2483526875847690, 11920928955078629

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..25.

FORMULA

G.f.: Sum_{k>=1} phi(k) * log(1 + 5*x^k) / k.

a(n) = -(1/n) * Sum_{k=1..n} (-5)^gcd(n,k).

Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A261569.

MATHEMATICA

Table[-(1/n) Sum[EulerPhi[n/d] (-5)^d, {d, Divisors[n]}], {n, 1, 25}]

nmax = 25; CoefficientList[Series[Sum[EulerPhi[k] Log[1 + 5 x^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest