A295126 Denominator of Sum_{d|n} mu(n/d)/d, where mu is the Möbius function A008683.

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

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