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Number of divisors of highly composite triangular numbers.
4

%I #10 Feb 03 2013 02:55:13

%S 1,2,4,6,9,16,18,20,24,36,40,48,90,112,128,144,162,168,192,240,320,

%T 480,576,648,768,1024,1280,1344,1512,1536,1728,1920,2304,2880,3072,

%U 3200,3456,3888,4480,5760,6144,6912,7680,8640,9216,13824,16128,23040,25088

%N Number of divisors of highly composite triangular numbers.

%H Charles R Greathouse IV and Donovan Johnson, <a href="/A101756/b101756.txt">Table of n, a(n) for n = 1..70</a> (first 55 terms from _Charles R Greathouse IV_).

%F a(n) = A000005(A076711(n)) = A000005(A000217(A101755(n))).

%o (PARI) t1=1;r=0;for(n=1,2e9,t2=n+1;t2=numdiv(t2/if(n%2,2,1));if(t1*t2>r,r=t1*t2;print1(r", "));t1=t2) \\ _Charles R Greathouse IV_, Feb 01 2013

%Y Cf. A076711, A101755.

%K nonn

%O 1,2

%A _Ray Chandler_, Dec 22 2004