A133949 a(n) = the number of "non-isolated divisors" of n(n+1)/2. A positive divisor k of n is non-isolated if either k-1 or k+1 also divides n.

0, 0, 3, 2, 0, 0, 2, 4, 0, 0, 3, 3, 0, 0, 6, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, 0, 5, 2, 0, 0, 2, 6, 0, 0, 10, 3, 0, 0, 8, 4, 0, 0, 2, 8, 0, 0, 4, 7, 0, 0, 3, 2, 0, 0, 6, 6, 0, 0, 5, 5, 0, 0, 8, 4, 0, 0, 2, 3, 0, 0, 4, 4, 0, 0, 5, 2, 0, 0, 4, 9, 0, 0, 5, 10, 0, 0, 6, 2, 0, 0, 4, 3, 0, 0, 10, 4, 0, 0, 8, 2, 0, 0, 2, 13

Offset: 1

Author

Leroy Quet, Sep 30 2007

Keywords

• nonn

Comments

a(k) = 0 for k mod 4 == {1,2}. - Ray Chandler

Links

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

Crossrefs

Cf. A133947, A133950, A063440.

Programs

Mathematica

Table[Length[Select[Divisors[n*(n + 1)/2], If[ # > 1, Mod[n*(n + 1)/2, #*(# - 1)] == 0] || Mod[n*(n + 1)/2, #*(# + 1)] == 0 &]], {n, 1, 80}] (* Stefan Steinerberger, Nov 01 2007 *)

Formula

a(n) = A063440(n) - A133950(n) = A132747(A000217(n)).

Extensions

More terms from Stefan Steinerberger, Nov 01 2007

Extended by Ray Chandler, Jun 23 2008