A211144 Smallest number k such that the sum of the distinct prime divisors of k equals n times a nontrivial integer power.

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(20) = 471 = 3*157, since the sum of the distinct prime 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. A008472, A213386.

Sequence in context: A332736 A162283 A180328 * A213386 A370403 A370405

Adjacent sequences: A211141 A211142 A211143 * A211145 A211146 A211147

Keyword

nonn

Author

Michel Lagneau, Jun 27 2012

Status

approved