A316274 Nonzero terms in row sums of the lower triangular part of a square matrix formed by Dirichlet convolution of adjacent columns in the square matrix A191898.

1, -4, -16, -9, -48, -25, -54, -128, 36, -49, -320, 144, -243, 100, 216, -121, -250, -768, 432, -169, 196, 400, 864, 225, -972, -1792, 1152, -289, 972, -686, -361, 784, 1200, 2592, 441, 484, 1000

Offset

1,2

Comments

The motivation for this sequence is expression 1 in Terence Tao's blog post "Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges".

Links

Table of n, a(n) for n=1..37.

Mats Granvik, Does the Dirichlet Inverse of the Euler totient function characterize asymptotic densities of prime gaps?.

Terence Tao, Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges.

Formula

a(n) = A298825(A001694(n)). - Mats Granvik, Oct 08 2018

Mathematica

Clear[nn, h, a, n, d, b, m];
nn = 500;
h = 1;
a[n_] := If[n < 1, 0, Sum[d MoebiusMu@d, {d, Divisors[n]}]];
TableForm[Transpose[Table[{n, a[n]}, {n, 1, nn}]]];
b = DeleteCases[
  Table[Sum[
    Sum[If[Mod[n, k] == 0, a[GCD[n/k, m]]*a[GCD[k, m + h]], 0], {k, 1,
       n}], {m, 1, n}], {n, 1, nn}], 0]

Crossrefs

Cf. A191898.

Sequence in context: A115054 A228561 A049208 * A337340 A061093 A067178

Adjacent sequences: A316271 A316272 A316273 * A316275 A316276 A316277

Keyword

sign

Author

Mats Granvik, Jun 28 2018

Status

approved