A295127 -id:A295127 - cp's OEIS frontend

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

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

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, ..., .

			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.

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

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

f:= n -> denom(add(numtheory:-mobius(n/k)/k, k=numtheory:-divisors(n))):
map(f, [$1..100]); # Robert Israel, Nov 16 2017

f[n_] := Block[{d = Divisors@ n}, Plus @@ (MoebiusMu[d]/Reverse@ d)]; Denominator@ Array[f, 70]
f[p_, e_] := -(p-1)/p^e; a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Jun 06 2025 *)

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI