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A343493 a(n) = 1 - Sum_{d|n, d < n} a(d - 1). 1
1, 1, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -1, 1, 0, 0, 0, 0, -2, 2, 0, 0, -2, 1, 1, 1, -1, 0, 0, 1, -1, 0, -1, 0, 0, 0, -1, 2, -2, 2, 0, 0, 0, 1, 1, 0, -2, 0, -1, 2, -1, 1, 0, 0, -2, 1, -1, 0, -1, 2, -1, 0, -2, 0, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,33

LINKS

Table of n, a(n) for n=0..90.

FORMULA

G.f. A(x) satisfies: A(x) = 1 / (1 - x) - x^2 * A(x^2) - x^3 * A(x^3) - x^4 * A(x^4) - ...

MATHEMATICA

a[n_] := a[n] = 1 - Sum[If[d < n, a[d - 1], 0], {d, Divisors[n]}]; Table[a[n], {n, 0, 90}]

nmax = 90; A[_] = 0; Do[A[x_] = 1/(1 - x) - Sum[x^k A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) //Normal, nmax + 1]; CoefficientList[A[x], x]

PROG

(Python)

from functools import lru_cache

from sympy import divisors

@lru_cache(maxsize=None)

def A343493(n): return 1-sum(A343493(d-1) for d in divisors(n) if d < n) # Chai Wah Wu, Apr 17 2021

CROSSREFS

Cf. A167865, A281487, A338639, A343371.

Sequence in context: A341775 A139032 A182035 * A095808 A281453 A079807

Adjacent sequences:  A343490 A343491 A343492 * A343494 A343495 A343496

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Apr 17 2021

STATUS

approved

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Last modified June 23 13:01 EDT 2021. Contains 345401 sequences. (Running on oeis4.)