

A211144


Smallest number k such that the sum of the distinct prime divisors of k equals n times a nontrivial integer power.


1



14, 15, 35, 39, 51, 95, 115, 87, 155, 111, 123, 215, 235, 159, 371, 183, 302, 335, 219, 471, 395, 415, 267, 623, 291, 303, 482, 327, 339, 791, 554, 1255, 635, 655, 411, 695, 662, 447, 698, 471, 734, 815, 835, 519, 1211, 543, 842, 1895, 579, 591, 914, 2167
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OFFSET

1,1


COMMENTS

Smallest k such that sopf(k) = n * m^q where m, q >= 2.
a(n) = A213386(n) except for n = 20, 32, 48, ...


LINKS

Table of n, a(n) for n=1..52.


EXAMPLE

a(20) = 471 = 3*157, and the sum of the divisors is 160= 20*2^3.


MAPLE

with (numtheory):
sopf:= proc(n) option remember;
add(i, i=factorset(n))
end:
a:= proc(n) local k, q;
for k while irem(sopf(k), n, 'q')>0 or
igcd (map(i>i[2], ifactors(q)[2])[])<2 do od; k
end:
seq (a(n), n=1..100);


CROSSREFS

Cf. A213386.
Sequence in context: A216680 A162283 A180328 * A213386 A041404 A041402
Adjacent sequences: A211141 A211142 A211143 * A211145 A211146 A211147


KEYWORD

nonn


AUTHOR

Michel Lagneau, Jun 27 2012


STATUS

approved



