A092509 - OEIS

A092509

Möbius transform of sequence A008475.

0, 2, 3, 2, 5, 0, 7, 4, 6, 0, 11, 0, 13, 0, 0, 8, 17, 0, 19, 0, 0, 0, 23, 0, 20, 0, 18, 0, 29, 0, 31, 16, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 42, 0, 0, 0, 53, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 32, 0, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 54, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = 0 if n is 1 or not a power of a prime;

a(n) = n if n is a prime;

a(n) = n*(1 -1/p) if n = p^k, k>= 2, p=prime.

a(n) = Sum_{d|n} A008683(d)*A008475(n/d). - Antti Karttunen, Nov 17 2017

MATHEMATICA

f[n_] := Plus @@ Map[Power @@ #1 &, FactorInteger[n]]; mt[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu /@ (n/d)*f /@ d)]; Table[ mt[n], {n, 93}] (* Robert G. Wilson v, Jan 12 2005 *)

PROG

(PARI)

A008475(n) = { my(f=factor(n)); vecsum(vector(#f~, i, f[i, 1]^f[i, 2])); };

A092509(n) = sumdiv(n, d, moebius(d)*A008475(n/d)); \\ Antti Karttunen, Nov 17 2017

CROSSREFS

Cf. A008475, A008683.

Sequence in context: A059051 A130069 A120007 * A214053 A214056 A368900

Adjacent sequences: A092506 A092507 A092508 * A092510 A092511 A092512

KEYWORD

nonn

AUTHOR

Leroy Quet, Dec 31 2004

EXTENSIONS

More terms from Robert G. Wilson v, Jan 13 2005

STATUS

approved