A346455 - OEIS

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..60.

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, 25] (* 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