A100635 Number of 2 X 2 matrices with elements in {1,2,...,n} such that LCMs of rows and columns are n.

1, 7, 7, 17, 7, 49, 7, 31, 17, 49, 7, 119, 7, 49, 49, 49, 7, 119, 7, 119, 49, 49, 7, 217, 17, 49, 31, 119, 7, 343, 7, 71, 49, 49, 49, 289, 7, 49, 49, 217, 7, 343, 7, 119, 119, 49, 7, 343, 17, 119, 49, 119, 7, 217, 49, 217, 49, 49, 7, 833, 7, 49, 119

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = 2*((e+1)^2) - 1.

Dirichlet g.f.: zeta(s)^3 * Product_{p prime} (1 + 4/p^s - 1/p^(2*s)). - Amiram Eldar, Sep 14 2023

Mathematica

Flatten[{1, Table[Product[2*((e+1)^2) - 1, {e, FactorInteger[n][[All, 2]]}], {n, 2, 100}]}] (* Vaclav Kotesovec, Sep 20 2020 *)

Prog

(PARI) A100635(n) = { my(f = factor(n), m = 1); for (k=1, #f~, m *= (2*((f[k, 2]+1)^2))-1; ); m; } \\ Antti Karttunen, May 25 2017

Crossrefs

Cf. A048691.

Sequence in context: A120682 A152910 A198439 * A292084 A168458 A165138

Adjacent sequences: A100632 A100633 A100634 * A100636 A100637 A100638

Keyword

mult,easy,nonn

Author

Vladeta Jovovic, Dec 03 2004

Status

approved