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!)
 A348223 a(n) = Sum_{d|n} (-1)^(sigma(d) - 1). 4
 1, 2, 0, 3, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, -2, 5, 0, 2, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, -4, 0, 6, -2, 0, -2, 3, 0, 0, -2, 0, 0, -4, 0, 0, -2, 0, 0, 0, 1, 2, -2, 0, 0, 0, -2, 0, -2, 0, 0, -6, 0, 0, -2, 7, -2, -4, 0, 0, -2, -4, 0, 4, 0, 0, -2, 0, -2, -4, 0, 0, 1, 0, 0, -6, -2, 0, -2, 0, 0, -4, -2, 0, -2, 0, -2, 0, 0, 2, -2, 3, 0, -4, 0, 0, -6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 FORMULA If p is an odd prime, a(p) = 0. G.f.: Sum_{k>=1} (-1)^(sigma(k) - 1) * x^k/(1 - x^k). From Bernard Schott, Oct 19 2021: (Start) If p is even prime = 2, a(2^k) = k+1 for k >= 0. If p is odd prime, a(p^even) = 1 and a(p^odd) = 0 (compare with formulas in A347992). (End) MATHEMATICA a[n_] := DivisorSum[n, (-1)^(DivisorSigma[1, #] - 1) &]; Array[a, 100] (* Amiram Eldar, Oct 08 2021 *) PROG (PARI) a(n) = sumdiv(n, d, (-1)^(sigma(d)-1)); (PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, (-1)^(sigma(k)-1)*x^k/(1-x^k))) CROSSREFS Cf. A000203, A347991, A347992. Sequence in context: A338504 A085200 A080024 * A035199 A035229 A348019 Adjacent sequences:  A348220 A348221 A348222 * A348224 A348225 A348226 KEYWORD sign AUTHOR Seiichi Manyama, Oct 08 2021 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 13:56 EST 2021. Contains 349445 sequences. (Running on oeis4.)