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A246469 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_(k)*p_(2)^d_(k-1)*…*p_(k)^d_(1), where p_(i) is the i-th prime. Sequence lists the numbers x such that y / x is integer. 2

%I #6 Sep 11 2014 18:17:08

%S 1,2,4,8,18,27,36,48,54,64,72,96,125,135,162,225,375,432,486,625,648,

%T 675,864,972,1225,1250,1323,1350,1575,1701,1715,1875,2250,2646,2835,

%U 2916,3375,3528,3645,3675,3750,3969,4116,4375,4536,4725,4860,5145,5488,5832

%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_(k)*p_(2)^d_(k-1)*…*p_(k)^d_(1), 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 A189398(x) / x is integer.

%H Paolo P. Lava, <a href="/A246469/b246469.txt">Table of n, a(n) for n = 1..1000</a>

%e x = 48 -> y = 2^4*3^8 = 104976 and 104976 / 48 = 2187.

%e x = 972 -> y = 2^9*3^7*5^2 = 27993600 and 27993600 / 972 = 28800.

%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(ilog10(n)+2-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, A246468.

%K nonn,base,easy

%O 1,2

%A _Paolo P. Lava_, Aug 27 2014

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Last modified February 25 02:17 EST 2024. Contains 370308 sequences. (Running on oeis4.)