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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.
2
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
1,2
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 19 2021
STATUS
approved