A133947 a(n) = the number of "non-isolated divisors" of n(n+1). A positive divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.

2, 3, 4, 4, 5, 5, 4, 6, 7, 4, 6, 6, 4, 8, 8, 4, 5, 5, 6, 11, 7, 4, 6, 8, 4, 5, 8, 4, 7, 7, 4, 8, 5, 4, 15, 6, 4, 5, 10, 6, 7, 7, 4, 12, 9, 4, 6, 9, 4, 7, 8, 4, 5, 10, 10, 9, 5, 4, 8, 8, 4, 7, 10, 6, 9, 5, 4, 6, 10, 4, 8, 8, 4, 7, 10, 4, 11, 5, 6, 13, 5, 4, 8, 15, 4, 5, 8, 4, 9, 13, 6, 6, 5, 4, 12, 6, 4, 9

Offset

1,1

Links

Ray Chandler, Table of n, a(n) for n=1..10000

Formula

a(n) = A092517(n) - A133948(n) = A132747(A002378(n)).

Mathematica

Table[Length[Select[Divisors[n*(n + 1)], If[ # > 1, Mod[n*(n + 1), #*(# - 1)] == 0] || Mod[n*(n + 1), #*(# + 1)] == 0 &]], {n, 1, 80}] (* Stefan Steinerberger, Nov 01 2007 *)

Crossrefs

Cf. A133948, A133949, A092517.

Sequence in context: A088527 A343400 A030602 * A082090 A060197 A116487

Adjacent sequences: A133944 A133945 A133946 * A133948 A133949 A133950

Keyword

nonn

Author

Leroy Quet, Sep 30 2007

Extensions

More terms from Stefan Steinerberger, Nov 01 2007

Extended by Ray Chandler, Jun 23 2008

Status

approved