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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
OFFSET
1,6
LINKS
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. 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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 08 2018
STATUS
approved