A085782 Numbers that can be written as a product of triangular numbers.

0, 1, 3, 6, 9, 10, 15, 18, 21, 27, 28, 30, 36, 45, 54, 55, 60, 63, 66, 78, 81, 84, 90, 91, 100, 105, 108, 120, 126, 135, 136, 150, 153, 162, 165, 168, 171, 180, 189, 190, 198, 210, 216, 225, 231, 234, 243, 252, 253, 270, 273, 276, 280, 300, 315, 324, 325, 330, 351

Offset: 1

Author

Jon Perry, Jul 23 2003

Keywords

• nonn

Comments

These are the numbers that appear at least once in A007425 (the number of ordered factorizations of n as n = r*s*t). - Matthew Vandermast, Jul 26 2003

Contains A085780 as a subsequence (exactly 2 factors); 27,54,81,... are the first elements in the complement. - M. F. Hasler, Apr 03 2008

The number of r-orthotopes of any size contained in a n1*n2*...*nr r-orthotope, where a(n)=t(n1)*t(n2)*...*t(nr) and t(k)=A000217(k). - Dimitri Boscainos, Aug 27 2015

Examples

			54 = 6*3*3 = t(3)*t(2)*t(2).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A007425, A085780, A334115.

Extensions

More terms from Max Alekseyev and Jon E. Schoenfield, Sep 04 2009