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A300252 Difference between arithmetic derivative (A003415) and its Möbius transform (A300251). 8
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 (list; graph; refs; listen; history; text; internal format)
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: A154794 A177264 A318366 * A305796 A020781 A007432

Adjacent sequences:  A300249 A300250 A300251 * A300253 A300254 A300255

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 08 2018

STATUS

approved

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Last modified November 17 18:42 EST 2018. Contains 317276 sequences. (Running on oeis4.)