A134978 Number of 2 X 2 singular integer matrices with entries from {2,...,n}.

0, 1, 6, 15, 28, 53, 74, 111, 152, 209, 246, 339, 384, 473, 582, 695, 756, 917, 986, 1175, 1340, 1493, 1578, 1855, 2008, 2193, 2398, 2683, 2792, 3185, 3302, 3603, 3880, 4129, 4446, 4943, 5084, 5365, 5698, 6231, 6388, 6973, 7138, 7615, 8172, 8517, 8698, 9431

Offset: 1

Author

Graziano Aglietti (mg5055(AT)mclink.it), Feb 04 2008

Keywords

• nice
• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A134506.

Programs

Mathematica

a[n_] := Sum[Sum[Sum[Boole[d <= n && d > 1 && b*c/d <= n && b*c > d], {d, Divisors[b*c]}], {c, 2, n}], {b, 2, n}];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Apr 25 2024, after Charles R Greathouse IV *)

PARI

a(n)=sum(b=2,n,sum(c=2,n,sumdiv(b*c,a, a<=n && a>1 && b*c/a<=n && b*c>a))) \\ Charles R Greathouse IV, Jun 17 2013

Formula

a(n) << n^(2+e) for all e > 0. - Charles R Greathouse IV, Jun 17 2013