A317581 - OEIS

%I #13 Jan 14 2022 16:03:41

%S 1,0,0,1,0,2,0,0,1,2,0,-2,0,2,2,1,0,-2,0,-2,2,2,0,4,1,2,0,-2,0,-6,0,0,

%T 2,2,2,7,0,2,2,4,0,-6,0,-2,-2,2,0,-4,1,-2,2,-2,0,4,2,4,2,2,0,16,0,2,

%U -2,1,2,-6,0,-2,2,-6,0,-12,0,2,-2,-2,2,-6,0,-4

%N a(1) = 1; a(n > 1) = 1 + Sum_{d|n, d<n} mu(n/d) a(d).

%C If p is prime, a(p^k) = 0 if k is odd, 1 if k is even. - _Robert Israel_, Aug 01 2018

%H Seiichi Manyama, <a href="/A317581/b317581.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= n -> 1 + add(numtheory:-mobius(n/d)*procname(d),d=numtheory:-divisors(n) minus {n}):

%p f(1):= 1:

%p map(f, [$1..100]); # _Robert Israel_, Aug 01 2018

%t a[n_]:=1+Sum[MoebiusMu[n/d]*a[d],{d,Most[Divisors[n]]}];

%t Array[a,100]

%o (Python)

%o from sympy import mobius, divisors

%o def A317581(n): return 1 + (0 if n == 1 else sum(mobius(n//d)*A317581(d) for d in divisors(n,generator=True) if d < n)) # _Chai Wah Wu_, Jan 14 2022

%Y Cf. A001678, A002033, A007554, A038046, A067824.

%K sign,eigen

%O 1,6

%A _Gus Wiseman_, Jul 31 2018