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

1,3

Links

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

Formula

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

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

a(n) = A010848(n) - A300720(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
A010848(n) = (n - A003557(n));
A300718(n) = sumdiv(n, d, moebius(n/d)*A010848(d));

Crossrefs

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

Sequence in context: A175542 A076686 A114810 * A093819 A089929 A131888

Adjacent sequences: A300715 A300716 A300717 * A300719 A300720 A300721

Keyword

nonn

Author

Antti Karttunen, Mar 11 2018

Status

approved