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Positive integers that cannot be written as a sum of a practical number and a nonagonal number.
1

%I #7 Jun 11 2024 01:44:46

%S 14,22,23,34,35,38,46,53,59,68,71,92,98,116,122,125,138,148,173,188,

%T 227,230,245,247,259,278,290,323,338,356,359,407,422,470,499,548,557,

%U 593,628,638,688,692,710,722,743,797,818,893,902,917,947,962,983,1013

%N Positive integers that cannot be written as a sum of a practical number and a nonagonal number.

%C Somu and Tran (2024) conjectured that there are finitely many such integers. It was also conjectured that 325808 is the largest such integer. This conjecture was checked up to 10^8.

%H Duc Van Khanh Tran, <a href="/A373611/b373611.txt">Table of n, a(n) for n = 1..186</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. A001106, A005153.

%K nonn,hard

%O 1,1

%A _Duc Van Khanh Tran_, Jun 10 2024