A349136 - OEIS

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A349136

Möbius transform of Kimberling's paraphrases, A003602.

1, 0, 1, 0, 2, 0, 3, 0, 3, 0, 5, 0, 6, 0, 4, 0, 8, 0, 9, 0, 6, 0, 11, 0, 10, 0, 9, 0, 14, 0, 15, 0, 10, 0, 12, 0, 18, 0, 12, 0, 20, 0, 21, 0, 12, 0, 23, 0, 21, 0, 16, 0, 26, 0, 20, 0, 18, 0, 29, 0, 30, 0, 18, 0, 24, 0, 33, 0, 22, 0, 35, 0, 36, 0, 20, 0, 30, 0, 39, 0, 27, 0, 41, 0, 32, 0, 28, 0, 44, 0, 36, 0, 30, 0, 36

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

OFFSET

1,5

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

FORMULA

a(n) = Sum_{d|n} A008683(d) * A003602(n/d).

a(1) = 1, a(n) = A000010(n)/2 for odd n > 1, a(n) = 0 for even n.

For all n >= 1, a(2*n-1) = A055034(2*n-1) = A072451(n).

a(n) = phi(n) - (1/2)*phi(2n), for n>1. - Ridouane Oudra, Jul 13 2023

Sum_{k=1..n} a(k) ~ (1/Pi^2)*n^2. - Amiram Eldar, Jul 15 2023

MAPLE