A222087 - OEIS

%I #10 Feb 18 2013 09:05:17

%S 1,2,6,14,15,20,22,24,33,38,46,49,51,52,62,63,86,87,91,92,93,95,118,

%T 119,121,141,142,143,145,147,148,153,158,159,165,166,169,183,198,206,

%U 210,215,217,219,244,247,249,253,262,267,270,278,279,286,287,295,301

%N Numbers n for which A222084(n)= A222084(A222085(n)).

%C 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 If we add also the restriction tau(n)=tau(sigma(n)) we have: 2, 52, 1525, 83667, 116162,…

%H Paolo P. Lava, <a href="/A222087/b222087.txt">Table of n, a(n) for n = 1..1000</a>

%e n=20; tau#(20)=4, sigma#(20)=12 and tau#(sigma#(20))=tau#(12)=4.

%p with(numtheory);

%p A222087:=proc(q)

%p local a,b,c,j,n,t,v;

%p print(1);

%p for n from 2 to q do

%p   a:=ifactors(n)[2]; b:=nops(a); c:=0; v:=0;

%p   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   a:=op(sort([op(divisors(n))])); b:=nops(divisors(n));

%p   for j from 1 to b do v:=v+a[j]; if a[j]=c then break; fi; od; t:=j;

%p   a:=ifactors(v)[2]; b:=nops(a); c:=0;

%p   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   a:=op(sort([op(divisors(v))])); b:=nops(divisors(v));

%p   for j from 1 to b do if a[j]=c then break; fi; od; if t=j then print(n);

%p fi; od; end:

%p A222087(10000000000);

%Y Cf. A000005, A000961, A001358, A003418, A005179, A024619, A034444, A077610, A222084, A222085.

%K nonn

%O 1,2

%A _Paolo P. Lava_, Feb 13 2013