cp's OEIS Frontend

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

%I A211144 #21 Oct 16 2019 01:48:34
%S A211144 14,15,35,39,51,95,115,87,155,111,123,215,235,159,371,183,302,335,219,
%T A211144 471,395,415,267,623,291,303,482,327,339,791,554,1255,635,655,411,695,
%U A211144 662,447,698,471,734,815,835,519,1211,543,842,1895,579,591,914,2167
%N A211144 Smallest number k such that the sum of the distinct prime divisors of k equals n times a nontrivial integer power.
%C A211144 Smallest k such that sopf(k) = n * m^q where m, q >= 2.
%C A211144 a(n) = A213386(n) except for n = 20, 32, 48, ...
%H A211144 Amiram Eldar, <a href="/A211144/b211144.txt">Table of n, a(n) for n = 1..10000</a>
%e A211144 a(20) = 471 = 3*157, since the sum of the distinct prime divisors is 160 = 20*2^3.
%p A211144 with (numtheory):
%p A211144 sopf:= proc(n) option remember;
%p A211144 add(i, i=factorset(n))
%p A211144 end:
%p A211144 a:= proc(n) local k, q;
%p A211144       for k while irem(sopf(k), n, 'q')>0 or
%p A211144       igcd (map(i->i[2], ifactors(q)[2])[])<2 do od; k
%p A211144     end:
%p A211144 seq (a(n), n=1..100);
%Y A211144 Cf. A008472, A213386.
%K A211144 nonn
%O A211144 1,1
%A A211144 _Michel Lagneau_, Jun 27 2012