The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A346455 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#9 by Susanna Cuyler at Mon Jul 19 18:29:44 EDT 2021

STATUS

proposed

approved

#8 by Giorgos Kalogeropoulos at Mon Jul 19 12:22:54 EDT 2021

STATUS

editing

proposed

#7 by Giorgos Kalogeropoulos at Mon Jul 19 12:22:46 EDT 2021

MATHEMATICA

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

STATUS

proposed

editing

#6 by Michel Marcus at Mon Jul 19 09:18:50 EDT 2021

STATUS

editing

proposed

#5 by Michel Marcus at Mon Jul 19 09:18:47 EDT 2021

PROG

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

STATUS

proposed

editing

#4 by Ilya Gutkovskiy at Mon Jul 19 08:54:20 EDT 2021

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Mon Jul 19 08:42:03 EDT 2021

CROSSREFS

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

#2 by Ilya Gutkovskiy at Mon Jul 19 08:30:20 EDT 2021

NAME

allocated for Ilya Gutkovskiya(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.

DATA

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.

CROSSREFS

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

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Jul 19 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Mon Jul 19 08:30:20 EDT 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved