cp's OEIS Frontend

A213420 Smallest number k such that the sum of prime factors of k (counted with multiplicity) is n times a square > 1.

%I A213420 #7 Oct 15 2019 07:41:46
%S A213420 4,15,35,39,51,95,115,87,155,111,123,215,235,159,371,183,302,335,219,
%T A213420 511,395,415,267,623,291,303,482,327,339,791,554,1415,635,655,411,695,
%U A213420 662,447,698,471,734,815,835,519,1211,543,842,1991,579,591,914,2167,2587
%N A213420 Smallest number k such that the sum of prime factors of k (counted with multiplicity) is n times a square > 1.
%C A213420 Smallest k such that sopfr(k) = n*q^2.
%C A213420 a(n) = A213386(n), except for n = 1, 105, 173, 213, 227, 287, …
%H A213420 Amiram Eldar, <a href="/A213420/b213420.txt">Table of n, a(n) for n = 1..10000</a>
%e A213420 a(105) = 3764 because 3764 = 2^2 * 941 and  the sum of prime factors  (counted with multiplicity) is 4 + 941 = 945 = 105*9 where 9 is a square.
%p A213420 with(numtheory):
%p A213420 sopfr:= proc(n) option remember;
%p A213420 add(i[1]*i[2], i=ifactors(n)[2])
%p A213420 end:
%p A213420 a:= proc(n) local k, p;
%p A213420 for k from 2 while irem(sopfr(k), n, 'p')>0 or
%p A213420 sqrt(p)<>floor(sqrt(p)) or p=1 do od; k
%p A213420 end:
%p A213420 seq (a(n), n=1..100);
%Y A213420 Cf. A213386, A212401.
%K A213420 nonn
%O A213420 1,1
%A A213420 _Michel Lagneau_, Jun 11 2012