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 A257669 #23 Dec 01 2019 06:00:57
%S A257669 1,1,2,3,1,2,4,5,1,1,1,4,2,3,6,1,1,3,1,2,1,1,1,11,1,1,1,5,1,2,3,5,1,1,
%T A257669 1,2,1,2,4,2,1,5,1,2,1,1,1,4,1,1,1,1,1,3,1,10,2,1,1,15,1,2,6,1,1,1,1,
%U A257669 2,1,1,1,7,1,2,1,1,1,2,1,4,1,1,1,5,1,1
%N A257669 Number of terms in the sigma(x) -> x subtree whose root is n.
%C A257669 For terms m of A007369, numbers m such that sigma(x) = m has no solution, as well as for m = 1, a(m) = 1.
%C A257669 See A257670 for more information, examples, etc. - _M. F. Hasler_, Nov 19 2019
%C A257669 Records are: a(1) = 1 = a(2), a(3) = 2, a(4) = 3, a(7) = 4, a(8) = 5, a(15) = 6, a(24) = 11, a(60) = 15, a(120) = 16, a(168) = 22 = a(336), a(360) = 26, a(480) = 39, a(1344) = 43, a(1512) = 54, a(1920) = 57, a(2016) = 65, a(2880) = 70, a(4800) = 80, a(5040) = 88, a(6552) = 93, a(8064) = 125, ... - _M. F. Hasler_, Nov 20 2019
%H A257669 M. F. Hasler, <a href="/A257669/b257669.txt">Table of n, a(n) for n = 1..10000</a>, Nov 20 2019
%H A257669 M. Alekseyev, <a href="https://home.gwu.edu/~maxal/gpscripts/invphi.gp">PARI/GP Scripts for Miscellaneous Math Problems: invsigma.gp</a>, Oct. 2005
%H A257669 G. L. Cohen and H. J. J. te Riele, <a href="http://projecteuclid.org/euclid.em/1047565640">Iterating the sum-of-divisors function</a>, Experimental Mathematics, 5 (1996), pp. 91-100.
%F A257669 a(A007369(n)) = 1.
%e A257669 For n = 2, a(2) = 1, since there is no x such that sigma(x) = 2, so the subtree with root 2 is reduced to a single node: 2.
%e A257669 For n = 3, since sigma(2) = 3, the tree with root 3 has 2 nodes: 2 and 3, hence a(3) = 2.
%o A257669 (PARI) A257669_vec(N)={my(C=Map(),s,c); vector(N,n,mapput(C,s=sigma(n), if(mapisdefined(C,s), mapget(C,s))+ c=if(mapisdefined(C,n), mapget(C,n) + mapdelete(C,n))+1);c)} \\ _M. F. Hasler_, Nov 20 2019
%o A257669 (PARI) apply( A257669(n)=if(n>1,vecsum(apply(self,invsigma(n))))+1, [1..99]) \\ See Alekseyev-link for invsigma(). - _M. F. Hasler_, Nov 20 2019, replacing earlier code from _Michel Marcus_
%Y A257669 Cf. A007369 (sigma(x) = n has no solution).
%Y A257669 Cf. A216200 (number of disjoint trees), A257348 (minimal nodes of all trees).
%Y A257669 Cf. A257670 (minimal representative of current tree).
%K A257669 nonn
%O A257669 1,3
%A A257669 _Michel Marcus_, May 03 2015