This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A373633 #11 Jun 13 2024 10:52:09
%S A373633 10,11,14,15,22,26,34,38,52,53,59,68,76,77,92,107,116,117,125,131,134,
%T A373633 149,152,158,164,173,179,184,185,187,188,206,212,227,230,236,245,248,
%U A373633 251,254,259,268,269,283,293,299,317,326,332,347,356,371,389,398,403
%N A373633 Positive integers that cannot be written as a sum of a practical number and a 15-gonal number.
%C A373633 Somu and Tran (2024) conjectured that there are finitely many such integers. It was also conjectured that 1486748 is the largest such integer. This conjecture was checked up to 10^8.
%H A373633 Duc Van Khanh Tran, <a href="/A373633/b373633.txt">Table of n, a(n) for n = 1..767</a>
%H A373633 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.
%t A373633 Lim=403;Lim15=Ceiling[Sqrt[2Lim/13]];
%t A373633 PracticalQ[nn_] := Module[{f, p, e, prod=1, ok=True}, If[nn<1 || (nn>1 && OddQ[n]), False, If[nn==1, True, f=FactorInteger[nn]; {p, e} = Transpose[f]; Do[If[p[[i]] > 1+DivisorSigma[1, prod], ok=False; Break[]]; prod=prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]];prac= Select[Range[Lim], PracticalQ] ;
%t A373633 seq={};Do[p15=i(13i-11)/2;p15i=prac+p15;AppendTo[seq,p15i],{i,0,Lim15}] (* sums of 15gonal and practical numbers *);
%t A373633 Complement[Range[Lim],Union[Flatten[seq]]] (* _James C. McMahon_, Jun 12 2024 *)
%Y A373633 Cf. A005153, A051867.
%K A373633 nonn,hard
%O A373633 1,1
%A A373633 _Duc Van Khanh Tran_, Jun 11 2024