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A374416 a(n) is the number of ways n can be written as a sum of a practical number and two nonagonal numbers.

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%I A374416 #6 Jul 31 2024 00:30:10
%S A374416 1,2,2,2,1,2,1,2,1,2,2,2,2,2,1,2,2,3,2,3,2,3,0,2,3,5,2,3,3,5,2,3,3,4,
%T A374416 1,3,4,3,2,3,4,5,2,2,3,2,1,5,6,5,3,4,3,5,3,5,5,4,2,4,4,2,4,5,5,7,4,2,
%U A374416 2,2,3,5,5,5,4,5,3,7,5,5
%N A374416 a(n) is the number of ways n can be written as a sum of a practical number and two nonagonal numbers.
%C A374416 Somu and Tran (2024) proved that a(n) > 0 for sufficiently large n.
%C A374416 Conjecture (checked up to 10^8): a(n) = 0 if and only if n = 23.
%H A374416 Duc Van Khanh Tran, <a href="/A374416/b374416.txt">Table of n, a(n) for n = 1..10000</a>
%H A374416 Sai Teja Somu and Duc Van Khanh Tran, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Somu/somu5.html">On sums of practical numbers and polygonal numbers</a>, Journal of Integer Sequences, 27(5), 2024.
%Y A374416 Cf. A001106, A005153.
%K A374416 nonn
%O A374416 1,2
%A A374416 _Duc Van Khanh Tran_, Jul 08 2024