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%I #6 Sep 11 2014 18:16:30
%S 1,2,4,8,12,16,24,36,48,54,81,96,128,135,144,162,225,288,375,486,576,
%T 625,648,675,768,972,1296,1575,1875,2187,2268,2625,2646,2688,3087,
%U 3136,3375,3528,3675,3888,3969,4116,4374,4802,5145,5292,5488,5625,6048,6174,7056
%N Given a number of k digits x = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1), consider y = p_(1)^d_(1)*p_(2)^d_(2)*…*p_(k)^d_(k), where p_(i) is the i-th prime. Sequence lists the numbers x such that y / x is integer.
%C a(n) = x such that A054842(x) / x is integer.
%H Paolo P. Lava, <a href="/A246468/b246468.txt">Table of n, a(n) for n = 1..1000</a>
%e x = 48 -> y = 2^8*3^4 = 20736 and 20736 / 48 = 432.
%e x = 972 -> y = 2^2*3^7*5^9 = 17085937500 and 17085937500 / 972 = 17578125.
%p with(numtheory):P:=proc(q) local a,b,k,n;
%p for n from 1 to q do a:=n; b:=1;
%p for k from 1 to ilog10(n)+1 do b:=b*ithprime(k)^(a mod 10); a:=trunc(a/10);
%p od; if type(b/n,integer) then print(n); fi; od; end: P(10^9);
%Y Cf. A054842, A189398, A246469.
%K nonn,base,easy
%O 1,2
%A _Paolo P. Lava_, Aug 27 2014
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