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A309369 a(n) = Sum_{d|n} phi(n/d)^d, where phi = Euler totient function (A000010). 7
1, 2, 3, 4, 5, 8, 7, 10, 15, 22, 11, 34, 13, 44, 105, 42, 17, 116, 19, 314, 357, 112, 23, 426, 1045, 158, 747, 1474, 29, 5290, 31, 594, 3069, 274, 24185, 6082, 37, 344, 9945, 67922, 41, 63542, 43, 12170, 303225, 508, 47, 74834, 279979, 1050022, 135201, 29098, 53, 309872, 4294345 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k>=1} phi(k)*x^k/(1 - phi(k)*x^k).
L.g.f.: -log(Product_{k>=1} (1 - phi(k)*x^k)^(1/k)).
a(p) = p for p prime.
a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^(gcd(k, n) - 1). - Seiichi Manyama, Mar 13 2021
MATHEMATICA
Table[Sum[EulerPhi[n/d]^d, {d, Divisors[n]}], {n, 1, 55}]
nmax = 55; CoefficientList[Series[Sum[EulerPhi[k] x^k/(1 - EulerPhi[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
nmax = 55; CoefficientList[Series[-Log[Product[(1 - EulerPhi[k] x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest
PROG
(PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(gcd(k, n)-1)); \\ Seiichi Manyama, Mar 13 2021
CROSSREFS
Sequence in context: A158979 A233249 A330573 * A091893 A074756 A240221
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 25 2019
STATUS
approved

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Last modified April 16 03:28 EDT 2024. Contains 371696 sequences. (Running on oeis4.)