A002053 -id:A002053 - OEIS

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Search: a002053 -id:a002053

Displaying 1-6 of 6 results found.

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A346456

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.

+0
2

3, 4, 5, 8, 9, 32, 9283, 9284, 9285, 9292, 9293, 9294, 9295, 9296, 9343, 9434, 9437, 9440, 9479, 9686, 9689, 9690, 9697, 9698, 9699, 9700, 9711, 9716, 9717, 9718, 9719, 9720, 9721, 9740, 9741, 9852, 9855, 9856, 9857, 10284, 10285, 10286, 10305, 10314, 10325, 10326, 10331, 10338

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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.

+0
3

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

(list; graph; refs; listen; history; text; internal format)

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.

+0
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

(list; graph; refs; listen; history; text; internal format)

A008836

Liouville's function lambda(n) = (-1)^k, where k is number of primes dividing n (counted with multiplicity).

+0
191

1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1

(list; graph; refs; listen; history; text; internal format)

A007421

Liouville's function: parity of number of primes dividing n (with multiplicity).
(Formerly M0067)

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7

2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1

(list; graph; refs; listen; history; text; internal format)

A002819

Liouville's function L(n) = partial sums of A008836.
(Formerly M0042 N0012)

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31

0, 1, 0, -1, 0, -1, 0, -1, -2, -1, 0, -1, -2, -3, -2, -1, 0, -1, -2, -3, -4, -3, -2, -3, -2, -1, 0, -1, -2, -3, -4, -5, -6, -5, -4, -3, -2, -3, -2, -1, 0, -1, -2, -3, -4, -5, -4, -5, -6, -5, -6, -5, -6, -7, -6, -5, -4, -3, -2, -3, -2, -3, -2, -3, -2, -1, -2, -3, -4, -3, -4, -5, -6, -7, -6, -7, -8, -7, -8, -9, -10, -9, -8, -9, -8, -7, -6

(list; graph; refs; listen; history; text; internal format)

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