A359165 -id:A359165 - cp's OEIS frontend

A359164 Difference between Kimberling's paraphrases and its Möbius transform.

0, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 4, 4, 1, 1, 5, 1, 3, 5, 6, 1, 2, 3, 7, 5, 4, 1, 8, 1, 1, 7, 9, 6, 5, 1, 10, 8, 3, 1, 11, 1, 6, 11, 12, 1, 2, 4, 13, 10, 7, 1, 14, 8, 4, 11, 15, 1, 8, 1, 16, 14, 1, 9, 17, 1, 9, 13, 18, 1, 5, 1, 19, 18, 10, 9, 20, 1, 3, 14, 21, 1, 11, 11, 22, 16, 6, 1, 23, 10, 12, 17, 24, 12

Offset: 1

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Antti Karttunen, Dec 22 2022

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65539

Cf. A003602, A008683, A111333, A349136.

Cf. also A349135, A359165.

A003602(n) = (1+(n>>valuation(n,2)))/2;
A349136(n) = sumdiv(n,d,moebius(d)*A003602(n/d));
A359164(n) = (A003602(n) - A349136(n));

a(n) = A003602(n) - A349136(n).
a(n) = Sum_{d|n, dA349136(d).
a(n) = -Sum_{d|n, dA008683(n/d)*A003602(d).
a((2^e)*prime(n)) = A111333(n) for all n >= 1 and e >= 1.

cp's OEIS Frontend

A359164 Difference between Kimberling's paraphrases and its Möbius transform.

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