cp's OEIS Frontend

A222086 a(n) is the least number k for which A000005(k)/A222084(k) = n.

%I A222086 #18 Feb 01 2015 09:40:37
%S A222086 1,30,360,840,11088,18018,1713600,32760,327600,350064,39437798400,
%T A222086 180180,8532905472000,47361600,720720,1750320
%N A222086 a(n) is the least number k for which A000005(k)/A222084(k) = n.
%C A222086 a(17) <= 214555365177753600. a(18) = 3423420, a(20) = 4084080, a(24) = 6126120, a(30) = 46558512, a(32) = 38798760. - _Hiroaki Yamanouchi_, Oct 03 2014
%e A222086 For k=18018, tau(k)=48: the 48 divisors of k are 1, 2, 3, 6, 7, 9, 11, 13, 14, 18, 21, 22, 26, 33, 39, 42, 63, 66, 77, 78, 91, 99, 117, 126, 143, 154, 182, 198, 231, 234, 273, 286, 429, 462, 546, 693, 819, 858, 1001, 1287, 1386, 1638, 2002, 2574, 3003, 6006, 9009, 18018.
%e A222086 The least common multiple of the first 8 divisors, (1, 2, 3, 6, 7, 9, 11, 13), is again 18018, but the least common multiple of the first 7 divisors, (1, 2, 3, 6, 7, 9, 11), is less than 18018.
%e A222086 Since tau#(k)=8 (see A222084 for the definition of tau#(n)), tau(k)/tau#(k) = 48/8 = 6, and since 18018 is the minimum number k to have this ratio, a(6)=18018.
%p A222086 with(numtheory);
%p A222086 A222086:=proc(q)
%p A222086 local a,b,c,d,j,n,t,v;
%p A222086 v:=array(1..100); for j from 1 to 100 do v[j]:=0; od; t:=0;
%p A222086 for n from 1 to q do
%p A222086   a:=ifactors(n)[2]; b:=nops(a); c:=0;
%p A222086   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 A222086   a:=op(sort([op(divisors(n))])); b:=nops(divisors(n));
%p A222086   for j from 1 to b do if a[j]=c then break; fi; od;
%p A222086   if type(tau(n)/j,integer)  then if tau(n)/j=t+1
%p A222086        then t:=t+1; lprint(t,n); while v[t+1]>0 do t:=t+1; lprint(t,v[t]); od;
%p A222086        else if tau(n)/j>t+1 then if v[tau(n)/j]=0 then v[tau(n)/j]:=n; fi; fi;
%p A222086 fi; fi; od; end:
%p A222086 A222086(1000000000000000);
%Y A222086 Cf. A000005, A000961, A001358, A003418, A005179, A024619, A034444, A077610, A222084, A222085.
%K A222086 nonn,more
%O A222086 1,2
%A A222086 _Paolo P. Lava_, Feb 12 2013
%E A222086 a(1) corrected and a(11), a(13) and a(14) added by _Hiroaki Yamanouchi_, Oct 03 2014