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

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

Formula

a(n) = A003602(n) - A349136(n).

a(n) = Sum_{d|n, d<n} A349136(d).

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

a((2^e)*prime(n)) = A111333(n) for all n >= 1 and e >= 1.

Prog

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

Crossrefs

Cf. A003602, A008683, A111333, A349136.

Cf. also A349135, A359165.

Sequence in context: A140191 A317840 A048207 * A105810 A063726 A290267

Adjacent sequences: A359161 A359162 A359163 * A359165 A359166 A359167

Keyword

nonn

Author

Antti Karttunen, Dec 22 2022

Status

approved