A346457 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, 4, 5, 8, 9, 32, 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

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..3223

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.

Maple

N:= 10000: # for values <= N
omega:= n -> nops(numtheory:-factorset(n)):
R:= map(n -> (-1)^omega(n), [$1..10000]):
S:= map(abs, ListTools:-PartialSums(R)):
m:= max(S):
V:= Vector(m):
for i from 1 to N do if S[i] > 0 and V[S[i]] = 0 then V[S[i]]:= i fi od:
convert(V, list); # Robert Israel, Oct 30 2023

Mathematica

Table[k=1; While[Abs[Sum[(-1)^PrimeNu@j, {j, k}]]!=n, k++]; k, {n, 30}] (* Giorgos Kalogeropoulos, Jul 19 2021 *)

Prog

(PARI) a(n) = my(k=1); while (abs(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, A346456.

Sequence in context: A067271 A268128 A064394 * A141220 A340762 A092022

Adjacent sequences: A346454 A346455 A346456 * A346458 A346459 A346460

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 19 2021

Status

approved