A213420 - OEIS

%I #7 Oct 15 2019 07:41:46

%S 4,15,35,39,51,95,115,87,155,111,123,215,235,159,371,183,302,335,219,

%T 511,395,415,267,623,291,303,482,327,339,791,554,1415,635,655,411,695,

%U 662,447,698,471,734,815,835,519,1211,543,842,1991,579,591,914,2167,2587

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

%C Smallest k such that sopfr(k) = n*q^2.

%C a(n) = A213386(n), except for n = 1, 105, 173, 213, 227, 287, …

%H Amiram Eldar, <a href="/A213420/b213420.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 with(numtheory):

%p sopfr:= proc(n) option remember;

%p add(i[1]*i[2], i=ifactors(n)[2])

%p end:

%p a:= proc(n) local k, p;

%p for k from 2 while irem(sopfr(k), n, 'p')>0 or

%p sqrt(p)<>floor(sqrt(p)) or p=1 do od; k

%p end:

%p seq (a(n), n=1..100);

%Y Cf. A213386, A212401.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jun 11 2012