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

Author

Antti Karttunen, Mar 08 2018

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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));

Formula

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

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