A300719 - OEIS

A300719

Difference between A003557 (n divided by largest squarefree divisor of n) and its Möbius transform.

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 3, 2, 1, 1, 1, 8, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 8, 1, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 2, 1, 1, 3, 16, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 5, 2, 1, 1, 1, 8, 9, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 16, 1, 7, 3, 6, 1, 1, 1, 4, 1

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OFFSET

1,8

LINKS

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

FORMULA

a(n) = -Sum_{d|n, d<n} A008683(n/d)*A003557(d).

a(n) = A003557(n) - A300717(n).

PROG

(PARI)

A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = max(0, f[i, 2]-1)); factorback(f); }; \\ From A003557

A300719(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A003557(d));