A318665 -id:A318665 - 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];

A318664 Numerators of the sequence whose Dirichlet convolution with itself yields A064664, the inverse permutation of EKG-sequence.

Original entry on oeis.org

1, 1, 5, 1, 5, -1, 7, 3, -1, -1, 10, 3, 14, -1, -7, 5, 33, 59, 37, 9, -10, -1, 43, -1, -1, -1, 181, 13, 57, 89, 61, 15, -29, -1, -45, 31, 67, -1, -41, 1, 37, 129, 81, 11, 301, -1, 89, 21, 1, 26, -97, 10, 50, -93, -47, -5, -109, -1, 107, -33, 115, -1, 411, 15, -43, 201, 64, 33, -127, 56, 67, 181, 69, -1, 283, 35, -31, 255, 151, 7

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, A305293, A305294, A318665 (denominators).

Cf. also A317929, A317930.

v064413 = readvec("b064413_upto65539_terms_only.txt"); \\ From b-file of A064413 prepared beforehand.
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) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A064664(n) - Sum_{d|n, d>1, d 1.

For n >= 2, a(2*A000040(n)) = -1.

cp's OEIS Frontend

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

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