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A036431 a(n) = number of positive integers b which, when added to the number of their divisors, tau(b), gives n.

%I A036431 #22 Oct 01 2021 11:08:47
%S A036431 0,1,0,1,1,0,2,0,1,1,0,2,1,1,1,0,0,2,2,0,2,0,0,1,2,2,0,1,0,1,2,1,1,1,
%T A036431 0,0,1,3,2,0,0,1,2,0,2,0,0,1,1,3,1,1,0,0,2,1,0,2,1,0,2,2,1,1,0,1,0,0,
%U A036431 3,0,1,1,2,2,1,0,0,2,0,0,3,1,0,1,1,3,0,0,1,2,2,0,0,0,1,2,1,2,2,0,0,1,1,1,2
%N A036431 a(n) = number of positive integers b which, when added to the number of their divisors, tau(b), gives n.
%C A036431 Invented by the HR concept formation program.
%H A036431 Robert Israel, <a href="/A036431/b036431.txt">Table of n, a(n) for n = 1..10000</a>
%H A036431 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 A036431 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 A036431 a(n) = |{b in N : b + tau(b) = n}|
%e A036431 a(7) = 2 because (i) 4+tau(4)=7 and (ii) 5+tau(5)=7.
%p A036431 N:= 200: # to get a(1)..a(N)
%p A036431 A:= Vector(N):
%p A036431 for b from 1 to N do
%p A036431   v:= b + numtheory:-tau(b);
%p A036431   if v <= N then A[v]:= A[v]+1 fi
%p A036431 od:
%p A036431 convert(A,list); # _Robert Israel_, Jun 10 2018
%o A036431 (PARI) a(n) = sum(i=1, n, i+numdiv(i) == n); \\ _Michel Marcus_, Oct 01 2021
%Y A036431 Cf. A036432.
%K A036431 nonn
%O A036431 1,7
%A A036431 Simon Colton (simonco(AT)cs.york.ac.uk)
%E A036431 a(87)=0 corrected by _Michel Marcus_, Aug 31 2013