A346455 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.

1, 52, 55, 56, 57, 58, 77, 88, 93, 94, 95, 96, 99, 100, 119, 124, 147, 148, 161, 162, 189, 206, 207, 208, 209, 210, 213, 214, 215, 216, 217, 218, 219, 226, 329, 330, 333, 334, 335, 394, 395, 416, 417, 424, 425, 428, 489, 514, 515, 544, 545, 546, 549, 554, 579, 584, 723, 724, 725, 800

Offset: 1

Author

Ilya Gutkovskiy, Jul 19 2021

Keywords

• nonn

Crossrefs

Cf. A001221, A002053, A051400, A051401, A051402, A051470, A060434, A076479, A174863, A275547, A346456, A346457.

Programs

Mathematica

a[n_]:=(k=1;While[Sum[(-1)^PrimeNu@j,{j,k}]!=n,k++];k);Array[a,25] (* Giorgos Kalogeropoulos, Jul 19 2021 *)

PARI

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

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.