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 A317581 a(1) = 1; a(n > 1) = 1 + Sum_{d|n, d
 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, 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, -2, 1, 2, -6, 0, -2, 2, -6, 0, -12, 0, 2, -2, -2, 2, -6, 0, -4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS If p is prime, a(p^k) = 0 if k is odd, 1 if k is even. - Robert Israel, Aug 01 2018 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 MAPLE f:= n -> 1 + add(numtheory:-mobius(n/d)*procname(d), d=numtheory:-divisors(n) minus {n}): f(1):= 1: map(f, [\$1..100]); # Robert Israel, Aug 01 2018 MATHEMATICA a[n_]:=1+Sum[MoebiusMu[n/d]*a[d], {d, Most[Divisors[n]]}]; Array[a, 100] PROG (Python) from sympy import mobius, divisors 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 CROSSREFS Cf. A001678, A002033, A007554, A038046, A067824. Sequence in context: A304650 A360670 A347992 * A359865 A035217 A357237 Adjacent sequences: A317578 A317579 A317580 * A317582 A317583 A317584 KEYWORD sign,eigen AUTHOR Gus Wiseman, Jul 31 2018 STATUS approved

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Last modified August 12 08:23 EDT 2024. Contains 375085 sequences. (Running on oeis4.)