A346456 a(n) is the smallest number k such that Sum_{j=1..k} (-1)^omega(j) = -n, where omega(j) is the number of distinct primes dividing j.

3, 4, 5, 8, 9, 32, 9283, 9284, 9285, 9292, 9293, 9294, 9295, 9296, 9343, 9434, 9437, 9440, 9479, 9686, 9689, 9690, 9697, 9698, 9699, 9700, 9711, 9716, 9717, 9718, 9719, 9720, 9721, 9740, 9741, 9852, 9855, 9856, 9857, 10284, 10285, 10286, 10305, 10314, 10325, 10326, 10331, 10338

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Formula

a(n) = min {k : Sum_{j=1..k} mu(rad(j)) = -n}, where mu is the Moebius function and rad is the squarefree kernel.

Mathematica

a[n_]:=(k=1; While[Sum[(-1)^PrimeNu@j, {j, k}]!=-n, k++]; k); Array[a, 6] (* Giorgos Kalogeropoulos, Jul 19 2021 *)

Prog

(PARI) a(n) = my(k=1); while (sum(j=1, k, (-1)^omega(j)) != -n, k++); k; \\ Michel Marcus, Jul 19 2021

Crossrefs

Cf. A001221, A002053, A051400, A051401, A051402, A051470, A060434, A076479, A174863, A275547, A346455, A346457.

Sequence in context: A327984 A066906 A125884 * A001602 A308197 A087012

Adjacent sequences: A346453 A346454 A346455 * A346457 A346458 A346459

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 19 2021

Status

approved