A133948 a(n) = the number of "isolated divisors" of n(n+1). A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.

0, 1, 2, 2, 3, 3, 4, 6, 5, 4, 6, 6, 4, 8, 12, 6, 7, 7, 6, 13, 9, 4, 10, 16, 8, 11, 16, 8, 9, 9, 8, 16, 11, 12, 21, 12, 4, 11, 22, 10, 9, 9, 8, 24, 15, 4, 14, 21, 14, 17, 16, 8, 11, 22, 22, 23, 11, 4, 16, 16, 4, 17, 32, 22, 23, 11, 8, 18, 22, 12, 16, 16, 4, 17, 26, 20, 21, 11, 14, 37, 15, 4, 16

Offset

1,3

Links

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

Formula

a(n) = A092517(n) - A133947(n) = A132881(A002378(n)).

Mathematica

Table[Length[Divisors[n*(n + 1)]] - 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. A133947, A133950, A092517.

Sequence in context: A302877 A303525 A368643 * A078935 A276774 A129768

Adjacent sequences: A133945 A133946 A133947 * A133949 A133950 A133951

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