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A342485
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a(n) = Sum_{d|n} phi(d)^(d+1).
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6
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1, 2, 17, 34, 4097, 146, 1679617, 262178, 60466193, 4198402, 1000000000001, 67109042, 1283918464548865, 470186664194, 281474976714769, 2251799813947426, 4722366482869645213697, 609359800476818, 12748236216396078174437377, 9223372036858974242
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^(n/gcd(k, n)).
G.f.: Sum_{k>=1} phi(k)^(k+1) * x^k/(1 - x^k).
If p is prime, a(p) = 1 + (p-1)^(p+1).
a(n) = Sum_{k=1..n} phi(gcd(n,k))^(gcd(n,k) + 1)/phi(n/gcd(n,k)). - Richard L. Ollerton, May 07 2021
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MATHEMATICA
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a[n_] := DivisorSum[n, EulerPhi[#]^(#+1) &]; Array[a, 20] (* Amiram Eldar, Mar 14 2021 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, eulerphi(d)^(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)^(k+1)*x^k/(1-x^k)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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