A368007 - OEIS

%I #17 Feb 06 2024 11:56:34

%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,25,27,28,29,31,

%T 33,35,37,38,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,

%U 77,79,81,83,85,87,89,91,93,95,97,99

%N Positive integers which cannot be written as a sum of two Zumkeller numbers.

%C Somu et al. (2023) proved that all but finitely many positive integers can be written as a sum of two Zumkeller numbers. Therefore, this sequence is finite.

%H Duc Van Khanh Tran, <a href="/A368007/b368007.txt">Table of n, a(n) for n = 1..1541</a>

%H Yuejian Peng and K. P. S. Bhaskara Rao, <a href="https://doi.org/10.1016/j.jnt.2012.09.020">On Zumkeller numbers</a>, Journal of Number Theory, 133(4), 2013, 1135-1155.

%H Sai Teja Somu, Andrzej Kukla, and Duc Van Khanh Tran, <a href="https://arxiv.org/abs/2310.14149">Some results on Zumkeller numbers</a>, arXiv:2310.14149 [math.NT], 2023.

%e All positive integers less than 12 are in the sequence because the smallest sum of two Zumkeller numbers is 6+6=12.

%Y Cf. A083207.

%K nonn,fini,full

%O 1,2

%A _Duc Van Khanh Tran_, Dec 07 2023