A246468 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 an integer.

1, 2, 4, 8, 12, 16, 24, 36, 48, 54, 81, 96, 128, 135, 144, 162, 225, 288, 375, 486, 576, 625, 648, 675, 768, 972, 1296, 1575, 1875, 2187, 2268, 2625, 2646, 2688, 3087, 3136, 3375, 3528, 3675, 3888, 3969, 4116, 4374, 4802, 5145, 5292, 5488, 5625, 6048, 6174, 7056

Offset: 1

Author

Paolo P. Lava, Aug 27 2014

Keywords

• nonn
• base
• easy

Comments

a(n) = x such that A054842(x)/x is an integer.

Examples

			x = 48 -> y = 2^8*3^4 = 20736 and 20736 / 48 = 432.
x = 972 -> y = 2^2*3^7*5^9 = 17085937500 and 17085937500 / 972 = 17578125.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A054842, A189398, A246469.

Programs

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(k)^(a mod 10); a:=trunc(a/10);
od; if type(b/n,integer) then print(n); fi; od; end: P(10^9);