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