A258258 Least number k having exactly n representations as a sum of the minimal number of triangular numbers, A000217.

1, 16, 40, 75, 52, 82, 166, 178, 147, 217, 334, 247, 481, 634, 457, 516, 921, 646, 1047, 1132, 822, 787, 2110, 1351, 1537, 1542, 1402, 1192, 1666, 1696, 2137, 1759, 1876, 2271, 1792, 2712, 2587, 3216, 3909, 2782, 3007, 2956, 4242, 3397, 3682, 4039, 3607, 3601

Offset: 1

Author

Martin Renner, May 24 2015

Keywords

• nonn

Comments

Fermat's polygonal number theorem states that every positive integer is a sum of at most n n-gonal numbers. The triangular case was proved in 1796 by Gauss (Eureka theorem), stating that every positive integer is the sum of at most three triangular numbers. This sequence is based on this representation as a sum of the minimal number of triangular numbers.

Examples

			a(2) = 16 = 1 + 15 = 6 + 10 is the smallest number with two representations.
a(3) = 40 = 1 + 3 + 36 = 6 + 6 + 28 = 10 + 15 + 15 is the smallest number with three representations.
a(4) = 75 = 3 + 6 + 66 = 3 + 36 + 36 = 10 + 10 + 55 = 15 + 15 + 45 is the smallest number with four representations.
		

Crossrefs

Cf. A141490, A258257.