A300718 Möbius transform of A010848, number of numbers k <= n such that at least one prime factor of n is not a prime factor of k.

0, 1, 2, 1, 4, 2, 6, 2, 4, 4, 10, 4, 12, 6, 8, 4, 16, 6, 18, 8, 12, 10, 22, 8, 16, 12, 12, 12, 28, 8, 30, 8, 20, 16, 24, 10, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22, 46, 16, 36, 20, 32, 24, 52, 18, 40, 24, 36, 28, 58, 16, 60, 30, 36, 16, 48, 20, 66, 32, 44, 24, 70, 20, 72, 36, 40, 36, 60, 24, 78, 32, 36, 40, 82, 24, 64, 42, 56, 40, 88, 24, 72

Offset: 1

Author

Antti Karttunen, Mar 11 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A000010, A008683, A003557, A010848, A300717, A300720.

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
A010848(n) = (n - A003557(n));
A300718(n) = sumdiv(n,d,moebius(n/d)*A010848(d));

Formula

a(n) = Sum_{d|n} A008683(n/d)*A010848(d).

a(n) = A000010(n) - A300717(n).

a(n) = A010848(n) - A300720(n).