A135615 a(n) = number of positive divisors of (n+1) that are each the average of a positive divisor of n and a positive divisor of (n+2).

2, 2, 3, 2, 3, 2, 4, 3, 4, 2, 3, 2, 4, 4, 4, 2, 3, 2, 5, 3, 4, 2, 4, 3, 4, 3, 4, 2, 3, 2, 4, 3, 4, 4, 5, 2, 4, 3, 4, 2, 3, 2, 4, 3, 4, 2, 4, 3, 5, 3, 4, 2, 5, 4, 6, 3, 4, 2, 3, 2, 4, 4, 6, 4, 4

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..2500

Formula

a(n) <= A000005(n+1). - Michel Marcus, Oct 23 2016

Example

The divisors of 5 are (1,5). The divisors of 6 are (1,2,3,6). And the divisors of 7 are (1,7). Looking at the divisors of 6, 1 is the average of 1 (from the divisors of 5) and 1 (from the divisors of 7). 3 is the average of 5 (from the divisors of 5) and 1 (from the divisors of 7). And 6 is the average of 5 (from the divisors of 5) and 7 (from the divisors of 7). 2 is not the average of any divisor of 5 and any divisor of 7. There are 3 divisors of 6 that are such averages, so a(5) = 3.

Mathematica

Table[Length[Intersection[Divisors[n + 1], Mean /@ Flatten[Outer[List, Divisors[n], Divisors[n + 2]], 1]]], {n, 1, 65}]  (* Brad Chalfan (brad(AT)chalfan.net), Aug 31 2010 *)

Crossrefs

Cf. A000005 (number of divisors).

Sequence in context: A326082 A067554 A135981 * A348856 A166469 A080226

Adjacent sequences: A135612 A135613 A135614 * A135616 A135617 A135618

Keyword

nonn

Author

Leroy Quet, Feb 28 2008

Extensions

More terms from Brad Chalfan (brad(AT)chalfan.net), Aug 31 2010

Status

approved