cp's OEIS Frontend

A317102 Powerful numbers whose distinct prime multiplicities are pairwise indivisible.

%I A317102 #14 Jun 24 2019 00:43:52
%S A317102 1,4,8,9,16,25,27,32,36,49,64,72,81,100,108,121,125,128,169,196,200,
%T A317102 216,225,243,256,288,289,343,361,392,432,441,484,500,512,529,625,648,
%U A317102 675,676,729,800,841,864,900,961,968,972,1000,1024,1089,1125,1152,1156,1225
%N A317102 Powerful numbers whose distinct prime multiplicities are pairwise indivisible.
%C A317102 A number is powerful if its prime multiplicities are all greater than 1.
%H A317102 Robert Israel, <a href="/A317102/b317102.txt">Table of n, a(n) for n = 1..3000</a>
%e A317102 144 = 2^4 * 3^2 is not in the sequence because 4 and 2 are not pairwise indivisible.
%p A317102 filter:= proc(n) local L,i,j,q;
%p A317102   L:= convert(map(t -> t[2],ifactors(n)[2]),set);
%p A317102   if min(L) = 1 then return false fi;
%p A317102   for j from 2 to nops(L) do
%p A317102     for i from 1 to j-1 do
%p A317102       q:= L[i]/L[j];
%p A317102       if q::integer or (1/q)::integer then return false fi;
%p A317102   od od;
%p A317102   true
%p A317102 end proc:
%p A317102 select(filter, [$4..10000]); # _Robert Israel_, Jun 23 2019
%t A317102 Select[Range[1000],And[Max@@Last/@FactorInteger[#]>=2,Select[Tuples[Last/@FactorInteger[#],2],And[UnsameQ@@#,Divisible@@#]&]=={}]&]
%Y A317102 Cf. A001694, A056239, A112798, A118914, A124010, A285572, A285573, A303362, A304713, A316475, A317101, A317616.
%K A317102 nonn
%O A317102 1,2
%A A317102 _Gus Wiseman_, Aug 01 2018
%E A317102 Definition corrected and a(1)=1 inserted by _Robert Israel_, Jun 23 2019