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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.
3
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
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
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