A076711 Highly composite triangular numbers.

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

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 sawed-off 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