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 A342618 a(n) = Sum_{d|n} phi(d)^(n+d+1). 1
 1, 2, 129, 514, 4194305, 9218, 470184984577, 17179877378, 609359740018689, 4402341478402, 100000000000000000000001, 1125899907563522, 137370551967459378662586974209, 36845784908492735250434, 9903520314283046597240029185 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..220 FORMULA a(n) = Sum_{k=1..n} phi(n/gcd(k,n))^(n + n/gcd(k,n)). G.f.: Sum_{k>=1} phi(k)^(2*k+1) * x^k/(1 - (phi(k) * x)^k). If p is prime, a(p) = 1 + (p-1)^(2*p+1). MATHEMATICA a[n_] := DivisorSum[n, EulerPhi[#]^(n + # + 1) &]; Array[a, 15] (* Amiram Eldar, Mar 17 2021 *) PROG (PARI) a(n) = sumdiv(n, d, eulerphi(d)^(n+d+1)); (PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n+n/gcd(k, n))); (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^(2*k+1)*x^k/(1-(eulerphi(k)*x)^k))) CROSSREFS Cf. A000010, A342608. Sequence in context: A090121 A003369 A303377 * A258806 A216358 A294274 Adjacent sequences:  A342615 A342616 A342617 * A342619 A342620 A342621 KEYWORD nonn AUTHOR Seiichi Manyama, Mar 16 2021 STATUS approved

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)