A037092 -id:A037092 - cp's OEIS frontend

A037048 Number of pairs {i,j}, i>1, j>1, such that ij < n^2.

0, 3, 9, 20, 33, 54, 77, 108, 142, 186, 228, 285, 342, 409, 481, 563, 644, 742, 837, 946, 1060, 1184, 1308, 1449, 1592, 1744, 1903, 2076, 2240, 2432, 2618, 2818, 3028, 3246, 3461, 3702, 3940, 4192, 4444, 4719, 4980, 5274, 5559

Offset: 2

Joe K. Crump (joecr(AT)carolina.rr.com)

nonn

			f(3)=3 because the only pairs of 2 numbers > 1 that are < 9 are (2,2) (2,3) (2,4).

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Cf. A034806, A037092.

Table[Sum[Floor[(n^2-1)/i]+1-i,{i,2,n}],{n,2,45}] (* Harvey P. Dale, Oct 10 2011 *)

Sum(floor((n^2-1)/i)+1-i, i=2..n)

A034806 Number of distinct sets of 2 numbers > 1 such that their product is between n^2 and (n+1)^2.

Original entry on oeis.org

2, 5, 9, 12, 17, 22, 28, 32, 40, 41, 50, 56, 63, 68, 78, 80, 91, 94, 102, 110, 120, 123, 131, 141, 148, 156, 166, 163, 179, 185, 195, 206, 214, 211, 229, 237, 248, 248, 265, 260, 281, 284, 296, 305, 314, 320, 333, 337

Offset: 2

Joe K. Crump (joecr(AT)carolina.rr.com)

nonn

			a(3)=5 because the only pairs of numbers > 1 that form a product between 3^2 and 4^2 are (2,5) (2,6) (3,4) (2,7) (3,5).

Michael De Vlieger, Table of n, a(n) for n = 2..1000
A. Cayley, Über die analytischen Figuren, welche in der Mathematik Bäume genannt werden und ihre Anwendung auf die Theorie chemischer Verbindungen, Chem. Ber. 8 (1875), 1056-1059. (Annotated scanned copy) [Annotation on p. 1057 references this A-number, but probably A034790 (which is given at the end of p. 1058) was meant instead. - _Andrey Zabolotskiy_, Nov 03 2023]

Cf. A037048, A037092.

Array[Sum[Floor[(2 # + PowerMod[#, 2, k])/k], {k, 2, #}] &, 48, 2] (* Michael De Vlieger, Jan 22 2018 *)

A034806(n) = sum(k=2,n,floor(((n+1)^2-1)/k)-floor(n^2/k)) \\ Michael B. Porter, Mar 13 2010

a(n) = Sum_{k=2..n} floor((2n + (n^2 mod k))/k).

cp's OEIS Frontend

A037048 Number of pairs {i,j}, i>1, j>1, such that ij < n^2.

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