A318664 -id:A318664 - cp's OEIS frontend

A323411 Dirichlet inverse of A064664, the inverse permutation of EKG-sequence.

1, -2, -5, 1, -10, 16, -14, -4, 19, 31, -20, -21, -28, 43, 89, 4, -33, -98, -37, -42, 125, 61, -43, 48, 76, 85, -87, -58, -57, -409, -61, -1, 179, 100, 255, 203, -67, 112, 251, 98, -74, -573, -81, -85, -559, 130, -89, -100, 146, -370, 296, -107, -100, 548, 347, 145, 332, 172, -107, 846, -115, 184, -783, 3, 506, -825, -128

Offset: 1

Antti Karttunen, Jan 13 2019

sign

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

Cf. A064413, A064664, A323412.

Cf. also A304526, A304527, A317843, A318664, A318665.

up_to = 32768;
v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ From precomputed file.
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);
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(dA064664(n)));
A323411(n) = v323411[n];

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

Original entry on oeis.org

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

Antti Karttunen, Sep 01 2018

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

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

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]);

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

cp's OEIS Frontend

A323411 Dirichlet inverse of A064664, the inverse permutation of EKG-sequence.

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