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%I #9 Mar 30 2012 19:00:28
%S 120,780,2016,3240,4560,5460,7140,7260,9180,10296,10440,12720,19110,
%T 21528,23220,26796,28680,28920,32640,34980,37128,39060,41328,49770,
%U 51360,56280,61776,64620,64980,73920,79800,97020,100128,103740,107880,114960,115440,122760
%N Triangular numbers n whose divisors can be partitioned into three disjoint sets whose sums are all sigma(n)/3.
%C Subsequence of A023197, A204830.
%C 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?
%e 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).
%Y Cf. A000217 (triangular numbers).
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Feb 03 2012
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