A349617 Dirichlet convolution of A064664 (the inverse permutation of EKG-permutation) with A055615 (Dirichlet inverse of n).

1, 0, 2, -1, 5, -6, 7, 2, -9, -11, 9, 2, 15, -15, -29, 1, 16, 18, 18, 5, -41, -21, 20, -4, -26, -29, 4, 7, 28, 64, 30, -3, -61, -34, -80, 9, 30, -38, -81, -6, 33, 92, 38, 14, 51, -44, 42, 10, -48, 53, -99, 6, 47, 4, -102, -17, -111, -58, 48, -4, 54, -62, 69, 2, -151, 146, 61, 18, -131, 157, 63, -3, 65, -68, 92, 18

Offset: 1

Author

Antti Karttunen, Nov 23 2021

Keywords

• sign
• look

Comments

Dirichlet convolution of this sequence with A000010 (Euler phi) is A304526 (Möbius transform of the inverse permutation of EKG-sequence).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to EKG sequence

Crossrefs

Cf. A055615, A064413, A064664, A349616 (Dirichlet inverse).

Cf. also A000010, A304526, A349614.

Programs

PARI

A055615(n) = (n*moebius(n));
v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ Data prepared with Chai Wah Wu's Dec 08 2014 Python-program given in A064413.
A064413(n) = v064413[n];
\\ Then its inverse A064664 is prepared:
m064664 = Map();
for(n=1,65539,mapput(m064664,A064413(n),n));
A064664(n) = mapget(m064664,n);
A349617(n) = sumdiv(n,d,A064664(d)*A055615(n/d));

Formula

a(n) = Sum_{d|n} A064664(d) * A055615(n/d).