A052346 Smallest number which is the sum of two positive triangular numbers in exactly n different ways.

1, 2, 16, 81, 471, 1056, 1381, 11781, 6906, 17956, 34531, 123256, 40056, 4462656, 305256, 448906, 200281, 1957231, 520731, 10563906, 1001406, 11222656, 539550781, 3454506, 1482081, 75865156, 7172606106, 8852431, 25035156, 334020781, 13018281, 38531031, 7410406, 7014160156

Offset: 0

Author

Christian G. Bower, Jan 23 2000

Keywords

• nonn

Comments

From Chai Wah Wu, Oct 20 2023: (Start)

Other terms:

a(35) = 42980356

a(36) = 19267056

a(38) = 1289707656

a(39) = 2782318906

a(40) = 37052031

a(41) = 256720506

a(42) = 325457031

a(45) = 221310781

a(47) = 550240551

a(48) = 60765331

a(50) = 2200089531

a(54) = 327539956

a(56) = 926300781

a(59) = 7629645156

a(60) = 481676406

a(63) = 4598740656

a(64) = 303826656

a(68) = 6418012656

a(71) = 4579579956

a(72) = 789949306

a(80) = 1519133281

a(81) = 9498658731

a(84) = 12041910156

a(90) = 8188498906

a(96) = 3220562556

a(108) = 13429138206

(End)

Examples

			a(4) = 471 because 471 is the sum of two positive triangular numbers in exactly 4 different ways (as 300+171, 351+120, 435+36, and 465 + 6), and there is no smaller number that has this property.
		

Crossrefs

Cf. A000217, A052343, A052344, A052345, A052347, A052348, A053587, A064816.

Extensions

a(27), a(28) = 8852431, 25035156; a(26) not yet found

a(26) from Donovan Johnson, Nov 17 2008

Name edited (added the qualifier "positive"), example edited, and a(29)-a(32) added by Jon E. Schoenfield, Jul 16 2017

a(33) from Chai Wah Wu, Oct 20 2023