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
KEYWORD
nonn,look
AUTHOR
Mats Granvik and Robert G. Wilson v, Nov 15 2017
STATUS
approved