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A295126 Denominator of Sum_{d|n} mu(n/d)/d, where mu is the Möbius function A008683. 2
1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 6, 13, 7, 15, 16, 17, 9, 19, 5, 7, 11, 23, 12, 25, 13, 27, 14, 29, 15, 31, 32, 33, 17, 35, 18, 37, 19, 13, 10, 41, 7, 43, 22, 45, 23, 47, 24, 49, 25, 51, 13, 53, 27, 11, 28, 19, 29, 59, 15, 61, 31, 21, 64, 65, 33, 67, 17, 69, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) <= n.

a(n) <> n when n is in A069209.

n == 0 (mod a(n)).

First occurrence of k: 1, 2, 3, 4, 5, 12, 7, 8, 9, 40, 11, 24, 13, 28, 15, 16, 17, 36, 19, 80, 63, 44, 23, 48, 25, ..., ;

First occurrence of k = a(n)/n: 1, 6, 21, 20, 55, 42, 203, 120, 171, 110, 253, 84, 689, 406, 465, 272, 1751, 342, ..., .

LINKS

Mats Granvik and Robert G. Wilson v, Table of n, a(n) for n = 1..10000

EXAMPLE

a(6) = 1 since mu(6)/1 + mu(3)/2 + mu(2)/3 + mu(1)/6 = 1 - 1/2 - 1/3 + 1/6 = 1/3.

MAPLE

f:= n -> denom(add(numtheory:-mobius(n/k)/k, k=numtheory:-divisors(n))):

map(f, [$1..100]); # Robert Israel, Nov 16 2017

MATHEMATICA

f[n_] := Block[{d = Divisors@ n}, Plus @@ (MoebiusMu[d]/Reverse@ d)]; Denominator@ Array[f, 70]

PROG

(PARI) a(n) = denominator(sumdiv(n, d, moebius(n/d)/d)); \\ Michel Marcus, Nov 17 2017

CROSSREFS

Cf. A008683, A069209, A191898, A007913, A023900, A173557, A295127 (numerator).

Sequence in context: A217434 A322035 A325943 * A235602 A304180 A327498

Adjacent sequences:  A295123 A295124 A295125 * A295127 A295128 A295129

KEYWORD

nonn,look

AUTHOR

Mats Granvik and Robert G. Wilson v, Nov 15 2017

STATUS

approved

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Last modified December 8 03:17 EST 2021. Contains 349590 sequences. (Running on oeis4.)