The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A303281 Expansion of (x/(1 - x)) * (d/dx) Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)). 4
 0, 2, 5, 13, 18, 30, 37, 61, 79, 99, 110, 146, 159, 187, 217, 281, 298, 352, 371, 431, 473, 517, 540, 636, 686, 738, 819, 903, 932, 1022, 1053, 1213, 1279, 1347, 1417, 1561, 1598, 1674, 1752, 1912, 1953, 2079, 2122, 2254, 2389, 2481, 2528, 2768, 2866, 3016, 3118, 3274, 3327, 3543, 3653 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sum of exponents in prime-power factorization of hyperfactorial: Product_{k=1..n} k^k (A002109). Partial sums of A066959. LINKS Table of n, a(n) for n=1..55. Eric Weisstein's World of Mathematics, Hyperfactorial Eric Weisstein's World of Mathematics, K-Function Index entries for sequences related to factorial numbers Index entries for sequences computed from exponents in factorization of n EXAMPLE a(4) = 13 because 2^2*3^3*4^4 = 2^10*3^3 and 10 + 3 = 13. MATHEMATICA nmax = 55; Rest[CoefficientList[Series[x/(1 - x) D[Sum[Boole[PrimePowerQ[k]] x^k/(1 - x^k), {k, 1, nmax}], x], {x, 0, nmax}], x]] Table[PrimeOmega[Hyperfactorial[n]], {n, 55}] Table[Sum[k PrimeOmega[k], {k, n}], {n, 55}] PROG (PARI) a(n) = sum(k=1, n, k*bigomega(k)); \\ Altug Alkan, Apr 20 2018 CROSSREFS Cf. A001222, A002109, A022559, A066959, A303279. Sequence in context: A333876 A156013 A112634 * A235204 A354706 A348392 Adjacent sequences: A303278 A303279 A303280 * A303282 A303283 A303284 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 20 2018 STATUS approved

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

Last modified June 15 18:41 EDT 2024. Contains 373410 sequences. (Running on oeis4.)