The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A097945 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A097945

a(n) = mu(n)*phi(n) where mu(n) is the Mobius function (A008683) and phi(n) is the Euler totient function (A000010).
(history; published version)

#56 by Susanna Cuyler at Sun Aug 22 09:25:31 EDT 2021

STATUS

proposed

approved

#55 by Antti Karttunen at Fri Aug 20 10:58:42 EDT 2021

STATUS

editing

proposed

#54 by Antti Karttunen at Fri Aug 20 10:58:05 EDT 2021

CROSSREFS

Cf. A000010, A003958, A007947, A008683, A008966, A023900, A047994, A143153, A173557, A322581.

#53 by Antti Karttunen at Fri Aug 20 10:57:16 EDT 2021

FORMULA

a(n) = A008966(n) * A023900(n) = abs(mu(n)) * A023900(n).

CROSSREFS

Cf. A000010, A003958, A007947, A008683, A023900, A047994, A143153, A173557, A322581.

STATUS

proposed

editing

#52 by Antti Karttunen at Fri Aug 20 10:52:57 EDT 2021

STATUS

editing

proposed

#51 by Antti Karttunen at Fri Aug 20 10:51:33 EDT 2021

FORMULA

a(n) = mu(n)*A000010(n) = mu(n)*A003958(n) = mu(n)*A047994(n) = mu(n)*A173557(n), where mu is Moebius Möbius mu function (A008683).

#50 by Antti Karttunen at Fri Aug 20 10:47:31 EDT 2021

FORMULA

From Antti Karttunen, Aug 20 2021: (Start)

a(n) = mu(n)*A000010(n) = mu(n)*A003958(n) = mu(n)*A047994(n), = mu(n)*A173557(n), where mu is Moebius mu function (A008683). a(n) = A322581(n)-A003958(n). - _Antti Karttunen_, Aug 20 2021

a(n) = A322581(n) - A003958(n).

(End)

CROSSREFS

Cf. A000010, A003958, A007947, A008683, A047994, A143153, A173557, A322581.

#49 by Antti Karttunen at Fri Aug 20 10:45:12 EDT 2021

FORMULA

a(n) = mu(n)*A000010(n) = mu(n)*A003958(n) = mu(n)*A047994(n), where mu is Moebius mu function (A008683). a(n) = A322581(n)-A003958(n). - Antti Karttunen, Aug 20 2021

CROSSREFS

Cf. A000010, A003958, A007947, A008683, A047994, A143153, A322581.

STATUS

approved

editing

#48 by Vaclav Kotesovec at Sun Jun 14 15:28:15 EDT 2020

STATUS

editing

approved

#47 by Vaclav Kotesovec at Sun Jun 14 15:28:10 EDT 2020

FORMULA

Sum_{k=1..n} abs(a(k)) ~ c * n^2, where c = A065464/2 = (1/2) * Product_{primes p} (1 - 2/p^2 + 1/p^3) = 0.21412475283854722... Equivalently, c = A065463 * 3 / Pi^2. - Vaclav Kotesovec, Jun 14 2020

STATUS

approved

editing