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.

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

Offset

1,2

Comments

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

Links

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

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)+2-k)^(a mod 10); a:=trunc(a/10);
od; if type(b/n, integer) then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A054842, A189398, A246468.

Sequence in context: A185178 A351471 A229718 * A092507 A347036 A297188

Adjacent sequences: A246466 A246467 A246468 * A246470 A246471 A246472

Keyword

nonn,base,easy

Author

Paolo P. Lava, Aug 27 2014

Status

approved