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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A303040 A302877 A303525 * 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

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)