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A222087 Numbers n for which A222084(n)= A222084(A222085(n)).

%I A222087 #10 Feb 18 2013 09:05:17
%S A222087 1,2,6,14,15,20,22,24,33,38,46,49,51,52,62,63,86,87,91,92,93,95,118,
%T A222087 119,121,141,142,143,145,147,148,153,158,159,165,166,169,183,198,206,
%U A222087 210,215,217,219,244,247,249,253,262,267,270,278,279,286,287,295,301
%N A222087 Numbers n for which A222084(n)= A222084(A222085(n)).
%C A222087 Similar to A037197 but using tau#(n), number of the least divisors of n whose LCM is equal to n, as defined in A222084, and sigma#(n), sum of the least divisors of n whose LCM is equal to n, as defined in A222085: tau#(n)=tau#(sigma#(n)).
%C A222087 If we add also the restriction tau(n)=tau(sigma(n)) we have: 2, 52, 1525, 83667, 116162,…
%H A222087 Paolo P. Lava, <a href="/A222087/b222087.txt">Table of n, a(n) for n = 1..1000</a>
%e A222087 n=20; tau#(20)=4, sigma#(20)=12 and tau#(sigma#(20))=tau#(12)=4.
%p A222087 with(numtheory);
%p A222087 A222087:=proc(q)
%p A222087 local a,b,c,j,n,t,v;
%p A222087 print(1);
%p A222087 for n from 2 to q do
%p A222087   a:=ifactors(n)[2]; b:=nops(a); c:=0; v:=0;
%p A222087   for j from 1 to b do if a[j][1]^a[j][2]>c then c:=a[j][1]^a[j][2]; fi; od;
%p A222087   a:=op(sort([op(divisors(n))])); b:=nops(divisors(n));
%p A222087   for j from 1 to b do v:=v+a[j]; if a[j]=c then break; fi; od; t:=j;
%p A222087   a:=ifactors(v)[2]; b:=nops(a); c:=0;
%p A222087   for j from 1 to b do if a[j][1]^a[j][2]>c then c:=a[j][1]^a[j][2]; fi; od;
%p A222087   a:=op(sort([op(divisors(v))])); b:=nops(divisors(v));
%p A222087   for j from 1 to b do if a[j]=c then break; fi; od; if t=j then print(n);
%p A222087 fi; od; end:
%p A222087 A222087(10000000000);
%Y A222087 Cf. A000005, A000961, A001358, A003418, A005179, A024619, A034444, A077610, A222084, A222085.
%K A222087 nonn
%O A222087 1,2
%A A222087 _Paolo P. Lava_, Feb 13 2013