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A333558 a(n) = Sum_{d|n} phi(d) * prime(d). 0
2, 5, 12, 19, 46, 41, 104, 95, 150, 165, 312, 203, 494, 365, 432, 519, 946, 545, 1208, 747, 990, 1105, 1828, 991, 1986, 1709, 2004, 1663, 3054, 1481, 3812, 2615, 3062, 3173, 3724, 2519, 5654, 4145, 4512, 3591, 7162, 3449, 8024, 4979, 5298, 6209, 9708, 4983, 9638, 6685 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..50.

FORMULA

G.f.: Sum_{k>=1} phi(k) * prime(k) * x^k / (1 - x^k).

a(n) = Sum_{k=1..n} prime(n/gcd(n,k)).

MATHEMATICA

Table[Sum[EulerPhi[d] Prime[d], {d, Divisors[n]}], {n, 1, 50}]

Table[Sum[Prime[n/GCD[n, k]], {k, 1, n}], {n, 1, 50}]

PROG

(PARI) a(n) = sumdiv(n, d, prime(d)*eulerphi(d)); \\ Michel Marcus, Mar 27 2020

CROSSREFS

Cf. A000010, A000040, A007445, A057660, A061150, A130029.

Sequence in context: A336462 A116728 A276478 * A095306 A258602 A327065

Adjacent sequences:  A333555 A333556 A333557 * A333559 A333560 A333561

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 26 2020

STATUS

approved

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Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)