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%I #22 Nov 10 2021 07:06:48
%S 1,3,6,8,11,16,17,20,22,23,27,29,35,36,40,41,44,46,47,53,54,57,60,65,
%T 67,68,70,76,77,79,80,83,87,88,92,93,94,100,101,106,107,114,116,117,
%U 121,125,128,131,132,134,135,140,142,148,155,156,157,158,161,164,166
%N Integers which cannot be written as k+tau(k) for some k.
%C Invented by the HR concept formation program.
%C Indices of 0's in A036431. - _Sean A. Irvine_, Nov 01 2020
%H Amiram Eldar, <a href="/A036434/b036434.txt">Table of n, a(n) for n = 1..10000</a>
%H Simon Colton, <a href="http://www.cs.uwaterloo.ca/journals/JIS/colton/joisol.html">Refactorable Numbers - A Machine Invention</a>, J. Integer Sequences, Vol. 2 (1999), Article 99.1.2.
%H Simon Colton, <a href="http://web.archive.org/web/20070831060523/http://www.dai.ed.ac.uk/homes/simonco/research/hr/">HR - Automatic Theory Formation in Pure Mathematics</a>.
%e None of 1,2,3,4,5,6,7 are such that k+tau(k)=8, so 8 is in the sequence.
%t m = 200; Complement[Range[m], Table[n + DivisorSigma[0, n], {n, 1, m}]] (* _Amiram Eldar_, Nov 10 2021 *)
%o (PARI) isok(n) = sum(k=1, n, k+numdiv(k) != n) == n; \\ _Michel Marcus_, Dec 08 2014
%Y Cf. A036431, A036438, A062249.
%K nonn
%O 1,2
%A Simon Colton (simonco(AT)cs.york.ac.uk)
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