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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A330018 a(n) = Sum_{d|n} (bigomega(d) - omega(d)). 1
 0, 0, 0, 1, 0, 0, 0, 3, 1, 0, 0, 2, 0, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 6, 1, 0, 3, 2, 0, 0, 0, 10, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 0, 12, 1, 2, 0, 2, 0, 6, 0, 6, 0, 0, 0, 4, 0, 0, 2, 15, 0, 0, 0, 2, 0, 0, 0, 13, 0, 0, 2, 2, 0, 0, 0, 12, 6, 0, 0, 4, 0, 0, 0, 6, 0, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Inverse Moebius transform of A046660. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA G.f.: Sum_{k>=1} A046660(k) * x^k / (1 - x^k). a(n) = A069264(n) - A062799(n). If m and n are coprime, a(m*n) = tau(m)*a(n) + tau(n)*a(m), where tau = A000005. - Robert Israel, Jun 12 2020 MAPLE N:= 100: # for a(1)..a(N) V:= Vector(N): for d from 1 to N do   v:= add(t[2]-1, t=ifactors(d)[2]);   L:= [seq(i, i=d..N, d)]:   V[L]:= map(`+`, V[L], v); od: convert(V, list); # Robert Israel, Jun 12 2020 MATHEMATICA a[n_] := Sum[PrimeOmega[d] - PrimeNu[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 90}] PROG (PARI) a(n) = sumdiv(n, d, bigomega(d) - omega(d)); \\ Michel Marcus, Jun 12 2020 CROSSREFS Cf. A001221, A001222, A005117 (positions of 0's), A046660, A062799, A069264, A268340. Sequence in context: A036876 A229038 A229143 * A065413 A107131 A027200 Adjacent sequences:  A330015 A330016 A330017 * A330019 A330020 A330021 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Nov 27 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 December 2 11:44 EST 2021. Contains 349440 sequences. (Running on oeis4.)