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

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

2,1

Links

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]

Formula

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

Example

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A037048, A037092.

Sequence in context: A354835 A086343 A056549 * A226822 A034307 A239876

Adjacent sequences: A034803 A034804 A034805 * A034807 A034808 A034809

Keyword

nonn

Author

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

Status

approved