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
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..3223
Crossrefs
Programs
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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
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Mathematica
Table[k=1;While[Abs[Sum[(-1)^PrimeNu@j,{j,k}]]!=n,k++];k,{n,30}] (* Giorgos Kalogeropoulos, Jul 19 2021 *) -
PARI
a(n) = my(k=1); while (abs(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.