A343370 a(1) = 1; a(n) = Sum_{d|n, d < n} (-1)^d * a(d).

1, -1, -1, -2, -1, -1, -1, -4, 0, -1, -1, -4, -1, -1, 1, -8, -1, -2, -1, -4, 1, -1, -1, -12, 0, -1, 0, -4, -1, -3, -1, -16, 1, -1, 1, -10, -1, -1, 1, -12, -1, -3, -1, -4, 0, -1, -1, -32, 0, -2, 1, -4, -1, -4, 1, -12, 1, -1, -1, -16, -1, -1, 0, -32, 1, -3, -1, -4, 1, -3, -1, -36, -1, -1, 0, -4, 1, -3, -1, -32, 0

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Formula

G.f.: x + Sum_{n>=1} (-1)^n * a(n) * x^(2*n) / (1 - x^n).

Maple

a:= proc(n) option remember; `if`(n<2, 1,
      add((-1)^d*a(d), d=numtheory[divisors](n) minus {n}))
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Apr 12 2021

Mathematica

a[1] = 1; a[n_] := a[n] = Sum[If[d < n, (-1)^d a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 70}]

Prog

(PARI)
memoA343370 = Map();
A343370(n) = if(1==n, 1, my(v); if(mapisdefined(memoA343370, n, &v), v, v = sumdiv(n, d, if(d<n, ((-1)^d)*A343370(d), 0)); mapput(memoA343370, n, v); (v))); \\ Antti Karttunen, Jan 02 2023

Crossrefs

Cf. A008683, A053850 (positions of 0's), A056913 (positions of 1's), A067856, A074206, A307778, A308077, A325144.

Sequence in context: A294616 A085384 A067856 * A160467 A353573 A345000

Adjacent sequences: A343367 A343368 A343369 * A343371 A343372 A343373

Keyword

sign

Author

Ilya Gutkovskiy, Apr 12 2021

Extensions

Data section extended up to a(81) by Antti Karttunen, Jan 02 2023

Status

approved