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A342542
a(n) = Sum_{k=1..n} phi(gcd(k, n))^(n/gcd(k, n) - 1).
4
1, 2, 3, 4, 5, 7, 7, 9, 15, 13, 11, 33, 13, 19, 105, 33, 17, 91, 19, 209, 469, 31, 23, 641, 1045, 37, 1627, 841, 29, 4217, 31, 673, 10461, 49, 29785, 10281, 37, 55, 49465, 68769, 41, 65197, 43, 12281, 529625, 67, 47, 273185, 279979, 1049661, 1049121, 52657, 53, 803647
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} phi(n/d) * phi(d)^(n/d-1).
If p is prime, a(p) = p.
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(n/#-1) &]; Array[a, 50] (* Amiram Eldar, Mar 15 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, eulerphi(gcd(k, n))^(n/gcd(k, n)-1));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*eulerphi(d)^(n/d-1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 15 2021
STATUS
approved