The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309368 a(n) = Sum_{d|n} prime(n/d)^d. 0
 2, 7, 13, 32, 43, 129, 145, 405, 660, 1417, 2079, 5999, 8233, 18903, 37271, 74912, 131131, 300239, 524355, 1139985, 2180263, 4372491, 8388691, 17853809, 33715580, 68704969, 136183123, 274127445, 536871021, 1100025921, 2147483775, 4343912079, 8638792645, 17309012967, 34380645545 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA G.f.: Sum_{k>=1} prime(k)*x^k/(1 - prime(k)*x^k). L.g.f.: -log(Product_{k>=1} (1 - prime(k)*x^k)^(1/k)). a(n) ~ 2^n. MATHEMATICA Table[Sum[Prime[n/d]^d, {d, Divisors[n]}], {n, 1, 35}] nmax = 35; CoefficientList[Series[Sum[Prime[k] x^k/(1 - Prime[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest nmax = 35; CoefficientList[Series[-Log[Product[(1 - Prime[k] x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest CROSSREFS Cf. A000040, A007445, A055225. Sequence in context: A231478 A320680 A079119 * A051748 A330452 A086904 Adjacent sequences:  A309365 A309366 A309367 * A309369 A309370 A309371 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jul 25 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 16:35 EST 2021. Contains 349394 sequences. (Running on oeis4.)