A318665 Denominators of the sequence whose Dirichlet convolution with itself yields A064664, the inverse permutation of EKG-sequence.

1, 1, 2, 1, 1, 2, 1, 1, 8, 2, 1, 2, 1, 2, 1, 1, 2, 8, 2, 2, 1, 2, 2, 2, 2, 2, 16, 2, 2, 4, 2, 2, 2, 2, 2, 8, 2, 2, 2, 1, 1, 4, 2, 1, 8, 2, 2, 2, 2, 1, 4, 1, 1, 16, 2, 2, 4, 2, 2, 4, 2, 2, 8, 1, 1, 4, 1, 2, 4, 1, 1, 8, 1, 2, 4, 2, 1, 4, 2, 1, 128, 2, 1, 4, 2, 2, 4, 1, 2, 16, 2, 2, 4, 2, 1, 4, 1, 1, 2, 8, 2, 4, 2, 2, 4

Offset: 1

Author

Antti Karttunen, Sep 01 2018

Keywords

• nonn
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to EKG sequence

Crossrefs

Cf. A064664, A304526, A304527, A318664 (numerators).

Programs

PARI

v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ From b-file of A064413 prepared previously.
A064413(n) = v064413[n];
m064664 = Map();
for(n=1,65539,mapput(m064664,A064413(n),n));
A064664(n) = mapget(m064664,n);
up_to = (2^14);
DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&dA317937.
v318664_65 = DirSqrt(vector(up_to, n, A064664(n)));
A318664(n) = numerator(v318664_65[n]);
A318665(n) = denominator(v318664_65[n]);

Formula

a(n) = denominator of f(n), where f(1) = 1, f(n) = (1/2) * (A064664(n) - Sum_{d|n, d>1, d 1.