A211537 Smallest number k such that the sum of prime factors of k (counted with multiplicity) equals n times a nontrivial integer power.

4, 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, 1263

Offset

1,1

Comments

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

a(n) = A211144(n) except for n = 55, 63, 73, ... Example: a(55) = 1964 = 2^2*491 but A211144(55) = 2631 = 3*877.

Links

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

Example

a(55) = 1964 = 2^2*491, since the sum of the prime divisors counted with multiplicity is 491+4 = 495 = 55*3^2.

Maple

sopfr:= proc(n) option remember;
add(i[1]*i[2], i=ifactors(n)[2])
end:
a:= proc(n) local k, q;
      for k while irem(sopfr(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. A001414, A211144.

Sequence in context: A124150 A054556 A113693 * A213420 A209345 A323452

Adjacent sequences: A211534 A211535 A211536 * A211538 A211539 A211540

Keyword

nonn

Author

Michel Lagneau, Jun 27 2012

Status

approved