A135545 a(n) = the largest proper divisor k of n where (k-1) and/or (k+1) divides (n+1).

1, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 2, 5, 2, 1, 2, 1, 4, 3, 2, 1, 6, 1, 2, 3, 2, 1, 2, 1, 4, 3, 2, 7, 2, 1, 2, 3, 2, 1, 2, 1, 4, 3, 2, 1, 8, 1, 2, 3, 2, 1, 6, 5, 4, 3, 2, 1, 2, 1, 2, 9, 4, 5, 2, 1, 4, 3, 2, 1, 2, 1, 2, 5, 2, 7, 2, 1, 10, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 4, 3, 2, 5, 2, 1, 2, 11, 2

Offset

3,2

Links

G. C. Greubel, Table of n, a(n) for n = 3..1000

Example

The proper divisors of 14 are 1,2,7. Now 2 is the largest of these divisors k where (k-1) and/or (k+1) divides 15 -- both (2-1) and (2+1) divide 15. So a(14) = 2.

Mathematica

Table[Max[Join[{1}, Select[Complement[Divisors[n], {1, n}], Mod[n + 1, # + 1] == 0 || Mod[n + 1, # - 1] == 0 &]]], {n, 3, 100}] (* Stefan Steinerberger, Aug 30 2008 *)

Crossrefs

Sequence in context: A352933 A372598 A276976 * A123317 A231557 A171453

Adjacent sequences: A135542 A135543 A135544 * A135546 A135547 A135548

Keyword

nonn

Author

Leroy Quet, May 10 2008

Extensions

More terms from Stefan Steinerberger, Aug 30 2008

Status

approved