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

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to EKG sequence

Formula

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

Prog

(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&&d<n, u[d]*u[n/d], 0)))/2); u}; \\ From A317937.
v318664_65 = DirSqrt(vector(up_to, n, A064664(n)));
A318664(n) = numerator(v318664_65[n]);
A318665(n) = denominator(v318664_65[n]);

Crossrefs

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

Sequence in context: A053734 A238904 A214501 * A057856 A117939 A321436

Adjacent sequences: A318662 A318663 A318664 * A318666 A318667 A318668

Keyword

nonn,frac

Author

Antti Karttunen, Sep 01 2018

Status

approved