A300252 Difference between arithmetic derivative (A003415) and its Möbius transform (A300251).

0, 0, 0, 1, 0, 2, 0, 4, 1, 2, 0, 8, 0, 2, 2, 12, 0, 10, 0, 10, 2, 2, 0, 24, 1, 2, 6, 12, 0, 17, 0, 32, 2, 2, 2, 32, 0, 2, 2, 32, 0, 21, 0, 16, 13, 2, 0, 64, 1, 16, 2, 18, 0, 42, 2, 40, 2, 2, 0, 56, 0, 2, 15, 80, 2, 29, 0, 22, 2, 25, 0, 88, 0, 2, 17, 24, 2, 33, 0, 88, 27, 2, 0, 72, 2, 2, 2, 56, 0, 73, 2, 28, 2, 2, 2, 160, 0, 22, 19, 62, 0, 41, 0, 64, 27

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A003415(n) - A300251(n).

a(n) = -Sum_{d|n, d<n} A008683(n/d)*A003415(d).

Prog

(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A300252(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A003415(d));

Crossrefs

Cf. A003415, A300245, A300251, A300253.

Cf. A001248 (seems to give the positions of 1's), A006881 (seems to give the positions of 2's).

Sequence in context: A177264 A326758 A318366 * A305796 A347961 A020781

Adjacent sequences: A300249 A300250 A300251 * A300253 A300254 A300255

Keyword

nonn

Author

Antti Karttunen, Mar 08 2018

Status

approved