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A100635
Number of 2 X 2 matrices with elements in {1,2,...,n} such that LCMs of rows and columns are n.
1
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
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
KEYWORD
mult,easy,nonn
AUTHOR
Vladeta Jovovic, Dec 03 2004
STATUS
approved