The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A228441 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A228441

G.f.: Sum_{k>0} -(-x)^k / (1 + x^k).
(history; published version)

#61 by Peter Bala at Tue Jan 23 15:05:25 EST 2024

FORMULA

a(n) = Sum_{d divides n} (-1)^(n + J_3(d)/phi(d)), where the Jordan totient function J_3(n) = A059477(n). - Peter Bala, Jan 23 2024

KEYWORD

sign,easy,mult,changed

STATUS

editing

approved

#60 by Peter Bala at Tue Jan 23 11:06:22 EST 2024

FORMULA

a(n) = Sum_{d divides n} (-1)^(n + J_3(d)/phi(d)), where the Jordan totient function J_3(n) = A059477(n). - Peter Bala, Jan 23 2024

STATUS

approved

editing

#59 by Joerg Arndt at Mon Sep 18 02:02:34 EDT 2023

STATUS

reviewed

approved

#58 by Michel Marcus at Mon Sep 18 01:29:13 EDT 2023

STATUS

proposed

reviewed

#57 by Amiram Eldar at Mon Sep 18 00:45:19 EDT 2023

STATUS

editing

proposed

#56 by Amiram Eldar at Mon Sep 18 00:29:06 EDT 2023

CROSSREFS

Cf. A000005, A007814, A016825, A051062, A046897, A051062, A099774, A321558.

#55 by Amiram Eldar at Mon Sep 18 00:28:47 EDT 2023

CROSSREFS

Cf. A000005, A007814, A016825, A099774, A051062, A046897, A099774, A321558.

#54 by Amiram Eldar at Mon Sep 18 00:26:59 EDT 2023

CROSSREFS

Cf. A000005, A007814, A016825, A099774, A046897, A321558.

#53 by Amiram Eldar at Mon Sep 18 00:25:32 EDT 2023

LINKS

P. Peter Bala, <a href="/A067856/a067856_1.pdf">A signed Dirichlet product of arithmetical functions</a>, 2019.

<a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>.

#52 by Amiram Eldar at Mon Sep 18 00:24:27 EDT 2023

FORMULA

a(n) = A000005(n) if n is odd, and A000005(n) * (A007814(n)-3)/(A007814(n)+1) if n is even. - Amiram Eldar, Sep 18 2023

MATHEMATICA

a[n_] := Module[{e = IntegerExponent[n, 2]}, DivisorSigma[0, n] * If[e == 0, 1, (e-3)/(e+1)]]; Array[a, 100] (* Amiram Eldar, Sep 18 2023 *)

KEYWORD

sign,easy,mult

STATUS

approved

editing