A295126 - OEIS

%I #30 Nov 19 2017 04:42:05

%S 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,

%T 29,15,31,32,33,17,35,18,37,19,13,10,41,7,43,22,45,23,47,24,49,25,51,

%U 13,53,27,11,28,19,29,59,15,61,31,21,64,65,33,67,17,69,35

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

%C a(n) <= n.

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

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

%C 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, ..., ;

%C 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, ..., .

%H Mats Granvik and Robert G. Wilson v, <a href="/A295126/b295126.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

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

%p map(f, [$1..100]); # _Robert Israel_, Nov 16 2017

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

%o (PARI) a(n) = denominator(sumdiv(n, d, moebius(n/d)/d)); \\ _Michel Marcus_, Nov 17 2017

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

%K nonn,look

%O 1,2

%A _Mats Granvik_ and _Robert G. Wilson v_, Nov 15 2017