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

Offset: 1

Author

Antti Karttunen, Mar 12 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A003557, A008683, A300717.

Programs

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,(dA003557(d));

Formula

a(n) = -Sum_{d|n, dA008683(n/d)*A003557(d).

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