A304526 Möbius transform of A064664, the inverse of EKG-sequence.

1, 1, 4, 1, 9, -2, 13, 5, 1, -2, 19, 2, 27, -2, -3, 9, 32, 7, 36, 8, -3, -2, 42, 4, 14, -2, 16, 12, 56, 15, 60, 14, -3, -2, 2, 15, 66, -2, -3, 17, 73, 23, 80, 21, 27, -2, 88, 20, 36, 23, -3, 19, 99, 20, 24, 18, -3, -2, 106, 18, 114, -2, 35, 33, 17, 41, 127, 32, -3, 33, 133, 24, 137, -2, 44, 34, 45, 44, 150, 23, 54, -2, 159, 27, 42, -2, -3, 33, 166, 25, 52

Offset: 1

Author

Antti Karttunen, May 18 2018

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32768
• Index entries for sequences related to EKG sequence

Crossrefs

Cf. A000010, A008683, A064423, A064664, A304527, A327867 (even bisection), A323411, A349617.

Programs

PARI

A304526(n) = sumdiv(n, d, moebius(n/d)*A064664(d));

Formula

a(n) = Sum_{d|n} A008683(n/d)*A064664(d).

a(n) = A064664(n) - A304527(n).

For all n >= 1, a(A000040(n)) = A064423(n).

For n >= 2, a(2*A000040(n)) = -2.

For n >= 3, a(3*A000040(n)) = -3.

a(n) = Sum_{d|n} A000010(n/d)*A349617(d). - Antti Karttunen, Jan 27 2024