A300251 Möbius transform of arithmetic derivative (A003415).

0, 1, 1, 3, 1, 3, 1, 8, 5, 5, 1, 8, 1, 7, 6, 20, 1, 11, 1, 14, 8, 11, 1, 20, 9, 13, 21, 20, 1, 14, 1, 48, 12, 17, 10, 28, 1, 19, 14, 36, 1, 20, 1, 32, 26, 23, 1, 48, 13, 29, 18, 38, 1, 39, 14, 52, 20, 29, 1, 36, 1, 31, 36, 112, 16, 32, 1, 50, 24, 34, 1, 68, 1, 37, 38, 56, 16, 38, 1, 88, 81, 41, 1, 52, 20, 43, 30, 84, 1, 50

Offset

1,4

Links

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

Formula

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

a(n) = A003415(n) - A300252(n).

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
A300251(n) = sumdiv(n, d, moebius(n/d)*A003415(d));

Crossrefs

Cf. A003415, A008683, A300245, A300252, A300253.

Sequence in context: A082495 A329385 A200476 * A016572 A072860 A068503

Adjacent sequences: A300248 A300249 A300250 * A300252 A300253 A300254

Keyword

nonn

Author

Antti Karttunen, Mar 08 2018

Status

approved