cp's OEIS Frontend

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

%I A211537 #26 Oct 15 2019 23:27:25
%S A211537 4,15,35,39,51,95,115,87,155,111,123,215,235,159,371,183,302,335,219,
%T A211537 471,395,415,267,623,291,303,482,327,339,791,554,1255,635,655,411,695,
%U A211537 662,447,698,471,734,815,835,519,1211,543,842,1895,579,591,914,2167,1263
%N A211537 Smallest number k such that the sum of prime factors of k (counted with multiplicity) equals n times a nontrivial integer power.
%C A211537 Smallest k such that sopfr(k) = n * m^q where m, q >= 2.
%C A211537 a(n) = A211144(n) except for n = 55, 63, 73, ... Example: a(55) = 1964 = 2^2*491 but A211144(55) = 2631 = 3*877.
%H A211537 Amiram Eldar, <a href="/A211537/b211537.txt">Table of n, a(n) for n = 1..10000</a>
%e A211537 a(55) = 1964 = 2^2*491, since the sum of the prime divisors counted with multiplicity is 491+4 = 495 = 55*3^2.
%p A211537 sopfr:= proc(n) option remember;
%p A211537 add(i[1]*i[2], i=ifactors(n)[2])
%p A211537 end:
%p A211537 a:= proc(n) local k, q;
%p A211537       for k while irem(sopfr(k), n, 'q')>0 or
%p A211537       igcd (map(i->i[2], ifactors(q)[2])[])<2 do od; k
%p A211537     end:
%p A211537 seq (a(n), n=1..100);
%Y A211537 Cf. A001414, A211144.
%K A211537 nonn
%O A211537 1,1
%A A211537 _Michel Lagneau_, Jun 27 2012