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

1,1

Comments

Subsequence of A023197, A204830.

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

Links

Table of n, a(n) for n=1..38.

Example

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).

Crossrefs

Cf. A000217 (triangular numbers).

Sequence in context: A052766 A052627 A251264 * A235551 A300664 A029573

Adjacent sequences: A206022 A206023 A206024 * A206026 A206027 A206028

Keyword

nonn

Author

Jaroslav Krizek, Feb 03 2012

Status

approved