A373686 - OEIS

%I #6 Jul 05 2024 17:08:46

%S 1,2,2,2,2,4,2,3,3,4,3,4,3,4,2,4,5,5,4,6,6,6,2,6,5,7,4,7,7,6,5,7,9,7,

%T 4,8,9,10,2,9,10,9,6,9,9,8,5,8,10,9,5,10,11,9,7,12,11,11,6,9,11,10,3,

%U 11,14,13,9,12,13,11,7,10,15,14,4,13,13,8,8,15

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

%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="/A373686/b373686.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. A000290, A005153.

%K nonn

%O 1,2

%A _Duc Van Khanh Tran_, Jun 13 2024