A349616 Dirichlet convolution of A000027 (the identity function) with the Dirichlet inverse of the inverse permutation of EKG-permutation.

1, 0, -2, 1, -5, 6, -7, -2, 13, 11, -9, -6, -15, 15, 49, 0, -16, -42, -18, -15, 69, 21, -20, 24, 51, 29, -48, -21, -28, -168, -30, -1, 97, 34, 150, 65, -30, 38, 141, 48, -33, -236, -38, -32, -317, 44, -42, -40, 97, -163, 163, -36, -47, 248, 192, 75, 183, 58, -48, 294, -54, 62, -443, 1, 301, -338, -61, -50, 211

Offset: 1

Author

Antti Karttunen, Nov 23 2021

Keywords

• sign

Links

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

Crossrefs

Cf. A000027, A064413, A064664, A323411, A349617 (Dirichlet inverse).

Cf. also A349613, A349614.

Programs

PARI

up_to = 32768;
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 was prepared:
m064664 = Map();
for(n=1,65539,mapput(m064664,A064413(n),n));
A064664(n) = mapget(m064664,n);
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA064664(n)));
A323411(n) = v323411[n];
A349616(n) = sumdiv(n,d,d*A323411(n/d));

Formula

a(n) = Sum_{d|n} d * A323411(n/d).