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

1,3

Links

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

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.

Prog

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

Crossrefs

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

Sequence in context: A372677 A003978 A122645 * A372676 A122646 A028496

Adjacent sequences: A378646 A378647 A378648 * A378650 A378651 A378652

Keyword

nonn,new

Author

Antti Karttunen, Dec 03 2024

Status

approved