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

1, 30, 360, 840, 11088, 18018, 1713600, 32760, 327600, 350064, 39437798400, 180180, 8532905472000, 47361600, 720720, 1750320

Offset

1,2

Comments

a(17) <= 214555365177753600. a(18) = 3423420, a(20) = 4084080, a(24) = 6126120, a(30) = 46558512, a(32) = 38798760. - Hiroaki Yamanouchi, Oct 03 2014

Links

Table of n, a(n) for n=1..16.

Example

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.
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.
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.

Maple

with(numtheory);
A222086:=proc(q)
local a, b, c, d, j, n, t, v;
v:=array(1..100); for j from 1 to 100 do v[j]:=0; od; t:=0;
for n from 1 to q do
  a:=ifactors(n)[2]; b:=nops(a); c:=0;
  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;
  a:=op(sort([op(divisors(n))])); b:=nops(divisors(n));
  for j from 1 to b do if a[j]=c then break; fi; od;
  if type(tau(n)/j, integer)  then if tau(n)/j=t+1
       then t:=t+1; lprint(t, n); while v[t+1]>0 do t:=t+1; lprint(t, v[t]); od;
       else if tau(n)/j>t+1 then if v[tau(n)/j]=0 then v[tau(n)/j]:=n; fi; fi;
fi; fi; od; end:
A222086(1000000000000000);

Crossrefs

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

Sequence in context: A339197 A107916 A091775 * A008656 A179717 A086864

Adjacent sequences: A222083 A222084 A222085 * A222087 A222088 A222089

Keyword

nonn,more

Author

Paolo P. Lava, Feb 12 2013

Extensions

a(1) corrected and a(11), a(13) and a(14) added by Hiroaki Yamanouchi, Oct 03 2014

Status

approved