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%I #21 Feb 24 2020 06:11:53
%S 1,2,7,38,122,2766,64686,1972296,5387768,56208248,753815160,
%T 130065181784,5398921735160
%N Sets a record for the number of positive integers which, when added to the number of their divisors, gives n.
%C Invented by the HR concept formation program.
%C a(13) > 10^13. - _Giovanni Resta_, Feb 24 2020
%H S. 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, #2.
%H S. 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>
%F Sets record for |{b in N : b + tau(b) = n}|.
%e 1 [ first with 0 ].
%e 2=1+tau(1) [ first with 1 ].
%e 7=4+tau(4) and 5+tau(5) [ first with 2 ].
%e 38=30+tau(30) and 32+tau(32) and 34+tau(34) [ first with 3 ].
%o (PARI) nbi(n) = {nb = 0; for (i = 1, n, if ((i + numdiv(i)) == n, nb++);); nb;}
%o lista(nn) = {rec = -1; for (n = 1, nn, new = nbi(n); if (new > rec, print1(n, ", "); rec = new;););} \\ _Michel Marcus_, Aug 31 2013
%Y Cf. A036431.
%K hard,nonn,nice,more
%O 0,2
%A Simon Colton (simonco(AT)cs.york.ac.uk)
%E More terms from Julian Richardson (julianr(AT)dai.ed.ac.uk), who has searched up to 100000000.
%E a(10)-a(11) from _Donovan Johnson_, Feb 19 2009
%E a(12) from _Giovanni Resta_, Feb 24 2020
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