A213020 - OEIS

%I #14 Nov 14 2020 01:28:15

%S 2,4,8,15,21,35,33,39,65,51,57,95,69,115,86,87,93,155,212,111,122,123,

%T 129,215,141,235,158,159,265,371,177,183,194,427,201,335,213,219,365,

%U 511,237,395,249,415,446,267,278,623,964,291,302,303,309,515,321,327

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

%C Smallest k such that sopfr(k) = n*p, p prime.

%H Alois P. Heinz, <a href="/A213020/b213020.txt">Table of n, a(n) for n = 1..5000</a>

%e a(19) = 212 because 212 = 2^2 * 53 => sum of prime factors = 2*2+53 = 57 = 19*3 where 3 is prime.

%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         not isprime(p) do od; k

%p     end:

%p seq (a(n), n=1..100); # _Alois P. Heinz_, Jun 03 2012

%t sopfr[n_] := Sum[Times @@ f, {f, FactorInteger[n]}];

%t a[n_] := For[k = 2, True, k++, If[PrimeQ[sopfr[k]/n], Return[k]]];

%t Array[a, 100] (* _Jean-François Alcover_, Nov 13 2020 *)

%o (PARI) sopfr(n) = my(f=factor(n)); sum(k=1,#f~,f[k,1]*f[k,2]); \\ A001414

%o isok(k, n) = my(dr = divrem(sopfr(k), n)); (dr[2]==0) && isprime(dr[1]);

%o a(n) = {my(k=2); while (!isok(k, n), k++); k;} \\ _Michel Marcus_, Nov 13 2020

%Y Cf. A001414, A100118, A213015, A213016.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jun 02 2012