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a(n) is the number of ways n can be written as a sum of a practical number and two octagonal numbers.
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%I #6 Jul 31 2024 00:30:16

%S 1,2,2,2,1,2,1,2,2,3,1,2,2,2,1,2,3,3,1,4,2,3,2,4,3,3,2,4,3,4,2,4,4,3,

%T 1,3,4,3,2,4,5,5,3,5,4,4,2,5,6,5,2,4,3,4,1,6,5,5,2,4,4,5,3,6,5,5,4,5,

%U 6,5,3,7,5,5,3,4,6,5,3,6

%N a(n) is the number of ways n can be written as a sum of a practical number and two octagonal numbers.

%C Somu and Tran (2024) proved that a(n) > 0 for sufficiently large n and conjectured that a(n) > 0 for all n > 0. The conjecture was checked up to 10^8.

%H Duc Van Khanh Tran, <a href="/A374415/b374415.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 Cf. A000567, A005153.

%K nonn

%O 1,2

%A _Duc Van Khanh Tran_, Jul 08 2024