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

Author

Michel Lagneau, Jun 27 2012

Keywords

• nonn

Comments

Smallest k such that sopf(k) = n * m^q where m, q >= 2.

a(n) = A213386(n) except for n = 20, 32, 48, ...

Examples

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

Links

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

Crossrefs

Cf. A008472, A213386.

Programs

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);