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A133950 a(n) = the number of "isolated divisors" of n(n+1)/2. A positive divisor k of n is isolated if neither k-1 nor k+1 divides n. 4

%I

%S 1,2,1,2,4,4,4,5,6,4,5,5,4,8,10,6,6,6,6,8,8,4,8,12,6,8,11,6,8,8,8,14,

%T 8,8,14,9,4,8,16,8,8,8,6,16,12,4,12,17,9,12,13,6,8,16,18,18,8,4,11,11,

%U 4,12,28,20,16,8,6,13,16,8,14,14,4,12,19,14,16,8,12,31,10,4,11,22,8,8,18

%N a(n) = the number of "isolated divisors" of n(n+1)/2. A positive divisor k of n is isolated if neither k-1 nor k+1 divides n.

%H Ray Chandler, <a href="/A133950/b133950.txt">Table of n, a(n) for n=1..10000</a>

%F a(n) = A063440(n) - A133949(n) = A132881(A000217(n)).

%e a(8)=5 because 36 (=8*9/2) has 5 isolated divisors: 6,9,12,18,36.

%p with(numtheory): b:=proc(n) local div, ISO, i: div:=divisors(n): ISO:={}: for i to tau(n) do if member(div[i]-1,div)=false and member(div[i]+1,div)=false then ISO:= `union`(ISO,{div[i]}) end if end do end proc: seq(nops(b((1/2)*j*(j+1))),j=1..80); # _Emeric Deutsch_, Oct 15 2007

%Y Cf. A133948, A133949, A063440.

%K nonn

%O 1,2

%A _Leroy Quet_, Sep 30 2007

%E More terms from _Emeric Deutsch_, Oct 15 2007

%E Extended by _Ray Chandler_, Jun 23 2008

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)