A378649 Möbius transform of A378647.

1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 8, 12, 6, 8, 8, 16, 10, 18, 10, 12, 10, 22, 20, 20, 12, 18, 12, 28, 20, 30, 16, 20, 16, 24, 32, 36, 18, 24, 26, 40, 24, 42, 20, 24, 22, 46, 48, 42, 20, 32, 24, 52, 30, 40, 32, 36, 28, 58, 64, 60, 30, 36, 32, 48, 32, 66, 32, 44, 28, 70, 88, 72, 36, 40, 36, 60, 36, 78, 60, 54, 40, 82

Offset: 1

Author

Antti Karttunen, Dec 03 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000010, A005101, A008683, A067824, A103977, A263837, A378644, A378647 (inverse Möbius transform).

Programs

PARI

A378649(n) = sumdiv(n,d,moebius(d)*A378647(n/d));

Formula

a(n) = Sum_{d|n} A008683(d)*A378647(n/d):

a(n) = (A378644(n)+A378647(n)) / 2.

a(n) = A000010(n) = phi(n) only when n is a non-abundant number (A263837), and apparently never when n is abundant, A005101.