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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 18 12:10 EDT 2019. Contains 321283 sequences. (Running on oeis4.)