

A076711


Highly composite triangular numbers.


3



1, 3, 6, 28, 36, 120, 300, 528, 630, 2016, 3240, 5460, 25200, 73920, 157080, 437580, 749700, 1385280, 1493856, 2031120, 2162160, 17907120, 76576500, 103672800, 236215980, 842161320, 3090906000, 4819214400, 7589181600, 7966312200, 13674528000, 20366564400
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OFFSET

1,2


LINKS

Charles R Greathouse IV and Donovan Johnson, Table of n, a(n) for n = 1..70 (terms < 10^23; first 55 terms from Charles R Greathouse IV).
Mark Dominus, More sawedoff shotguns, 2007.
David Eppstein, Triangular numbers with many factors, 2007.
Shyam Sunder Gupta Fascinating Triangular Numbers.


EXAMPLE

a(4)=28: 28 is a triangular number and has 6 divisors. Number of divisors of all triangular numbers less than 28 is less than 6. So 28 is a highly composite triangular number.


PROG

(PARI) r=0; for(n=1, 1e7, t=if(n%2, numdiv(n)*numdiv((n+1)/2), numdiv(n/2)*numdiv(n+1)); if(t>r, r=t; print1(n*(n+1)/2", "))) \\ Charles R Greathouse IV, Feb 01 2013


CROSSREFS

Cf. A101755, A101756.
Sequence in context: A247016 A083675 A085076 * A075088 A102428 A128056
Adjacent sequences: A076708 A076709 A076710 * A076712 A076713 A076714


KEYWORD

nonn


AUTHOR

Shyam Sunder Gupta, Oct 26 2002


STATUS

approved



