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A034806 Number of distinct sets of 2 numbers > 1 such that their product is between n^2 and (n+1)^2. 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 (list; graph; refs; listen; history; text; internal format)
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)

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: A276217 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

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Last modified February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)