A206025 Triangular numbers k whose divisors can be partitioned into three disjoint sets whose sums are all sigma(k)/3.

120, 780, 2016, 3240, 4560, 5460, 7140, 7260, 9180, 10296, 10440, 12720, 19110, 21528, 23220, 26796, 28680, 28920, 32640, 34980, 37128, 39060, 41328, 49770, 51360, 56280, 61776, 64620, 64980, 73920, 79800, 97020, 100128, 103740, 107880, 114960, 115440, 122760

Offset: 1

Author

Jaroslav Krizek, Feb 03 2012

Keywords

• nonn

Comments

Divisors of triangular number k = 120 can be partitioned into three disjoint sets whose sums are all sigma(k)/3 and this value is triangular numbers (=120). Are there other such triangular numbers?

Examples

			Triangular number 780 is in sequence because sigma(780)/3 = 784 = 4+780 = 2+5+6+10+12+13+15+20+26+30+39+52+60+65+78+156+195 = 1+3+130+260+390 (summands are all divisors of 780).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..398

Crossrefs

Intersection of A000217 and A204830.

Subsequence of A023197.

Cf. A000203.