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 A333232 #11 Mar 12 2020 18:58:01 %S A333232 5865,7395,10005,15045,28815,37995,45645,50235,99705,134895,170085, %T A333232 275655,310845,347565,391935,436305,470235,486795,521985,530265, %U A333232 590295,613785,627555,635205,658155,662745,707115,791265,797385,830415,835635,873885,887655,979455,994755 %N A333232 Terms of A051488 that do not belong to A083207. %H A333232 Giovanni Resta, <a href="/A333232/b333232.txt">Table of n, a(n) for n = 1..10000</a> %H A333232 K. P. S. Bhaskara Rao and Yuejian Peng, <a href="https://doi.org/10.1016/j.jnt.2012.09.020">On Zumkeller Numbers</a>, Journal of Number Theory, Volume 133, Issue 4, April 2013, pp. 1135-1155. %t A333232 (* First 200000 terms of A051488 *) %t A333232 a051488=Select[Range[200000],EulerPhi[#]<EulerPhi[#-EulerPhi[#]]&]; %t A333232 (* Fast test to sift out the "easiest" Zumkeller numbers, see Proposition 17, Rao/Peng link *) %t A333232 d[n_]:=Divisors[n]; fQ[n_]:=EvenQ[DivisorSigma[1,n]]; %t A333232 gQ[n_]:=Union[Table[d[n][[i+1]]<=2*d[n][[i]],{i,1,Length[d[n]]-1}]]=={True}; znQ[n_]:=fQ[n]&&gQ[n]; t1=Select[a051488,!znQ[#]&]; %t A333232 (* Comprehensive test to sift out the remaining Zumkeller numbers, code by _T. D. Noe_ at A083207 *) %t A333232 zQ[n_]:=Module[{d=Divisors[n],t,ds,x},ds=Plus@@d;If[Mod[ds,2]>0,False,t=CoefficientList[Product[1+x^i,{i,d}],x];t[[1+ds/2]]>0]]; t2=Select[t1,!zQ[#]&] %Y A333232 Cf. A000010, A051488, A083207. %K A333232 nonn %O A333232 1,1 %A A333232 _Ivan N. Ianakiev_, Mar 12 2020 %E A333232 Terms a(12) and beyond from _Giovanni Resta_, Mar 12 2020