

A246469


Given a number of k digits x = d_(k)*10^(k1) + d_(k1)*10^(k2) + … + d_(2)*10 + d_(1), consider y = p_(1)^d_(k)*p_(2)^d_(k1)*…*p_(k)^d_(1), where p_(i) is the ith prime. Sequence lists the numbers x such that y / x is integer.


2



1, 2, 4, 8, 18, 27, 36, 48, 54, 64, 72, 96, 125, 135, 162, 225, 375, 432, 486, 625, 648, 675, 864, 972, 1225, 1250, 1323, 1350, 1575, 1701, 1715, 1875, 2250, 2646, 2835, 2916, 3375, 3528, 3645, 3675, 3750, 3969, 4116, 4375, 4536, 4725, 4860, 5145, 5488, 5832
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OFFSET

1,2


COMMENTS

a(n) = x such that A189398(x) / x is integer.


LINKS



EXAMPLE

x = 48 > y = 2^4*3^8 = 104976 and 104976 / 48 = 2187.
x = 972 > y = 2^9*3^7*5^2 = 27993600 and 27993600 / 972 = 28800.


MAPLE

with(numtheory):P:=proc(q) local a, b, k, n;
for n from 1 to q do a:=n; b:=1;
for k from 1 to ilog10(n)+1 do b:=b*ithprime(ilog10(n)+2k)^(a mod 10); a:=trunc(a/10);
od; if type(b/n, integer) then print(n); fi; od; end: P(10^9);


CROSSREFS



KEYWORD

nonn,base,easy


AUTHOR



STATUS

approved



