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

1,3

Comments

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

Links

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

Formula

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

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 *)

Crossrefs

Cf. A133947, A133950, A063440.

Sequence in context: A231724 A214851 A245203 * A139808 A055654 A170849

Adjacent sequences: A133946 A133947 A133948 * A133950 A133951 A133952

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