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A133947 a(n) = the number of "non-isolated divisors" of n(n+1). A positive divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n. 3

%I

%S 2,3,4,4,5,5,4,6,7,4,6,6,4,8,8,4,5,5,6,11,7,4,6,8,4,5,8,4,7,7,4,8,5,4,

%T 15,6,4,5,10,6,7,7,4,12,9,4,6,9,4,7,8,4,5,10,10,9,5,4,8,8,4,7,10,6,9,

%U 5,4,6,10,4,8,8,4,7,10,4,11,5,6,13,5,4,8,15,4,5,8,4,9,13,6,6,5,4,12,6,4,9

%N a(n) = the number of "non-isolated divisors" of n(n+1). A positive divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.

%H Ray Chandler, <a href="/A133947/b133947.txt">Table of n, a(n) for n=1..10000</a>

%F a(n) = A092517(n) - A133948(n) = A132747(A002378(n)).

%t Table[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 *)

%Y Cf. A133948, A133949, A092517.

%K nonn

%O 1,1

%A _Leroy Quet_, Sep 30 2007

%E More terms from _Stefan Steinerberger_, Nov 01 2007

%E Extended by _Ray Chandler_, Jun 23 2008

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)