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 A342619 a(n) = Sum_{d|n} phi(n/d)^(n-d+1). 2
 1, 2, 9, 18, 1025, 98, 279937, 65666, 10077825, 1310722, 100000000001, 16780802, 106993205379073, 91424858114, 35184439199745, 281476050460674, 295147905179352825857, 118486616186882, 708235345355337676357633, 1152921796664688642, 46005120518729441509377, 11000000000000000000002 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..388 FORMULA a(n) = Sum_{k=1..n} phi(n/gcd(k,n))^(n - gcd(k,n)). G.f.: Sum_{k>=1} (phi(k) * x)^k/(1 - phi(k)^(k-1) * x^k). If p is prime, a(p) = 1 + (p-1)^p. MATHEMATICA a[n_] := DivisorSum[n, EulerPhi[n/#]^(n - # + 1) &]; Array[a, 20] (* Amiram Eldar, Mar 17 2021 *) PROG (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)^(n-d+1)); (PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n-gcd(k, n))); (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (eulerphi(k)*x)^k/(1-eulerphi(k)^(k-1)*x^k))) CROSSREFS Cf. A000010, A342612. Sequence in context: A297470 A075537 A342473 * A342471 A180852 A075340 Adjacent sequences:  A342616 A342617 A342618 * A342620 A342621 A342622 KEYWORD nonn AUTHOR Seiichi Manyama, Mar 16 2021 STATUS approved

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Last modified December 2 12:01 EST 2021. Contains 349440 sequences. (Running on oeis4.)