cp's OEIS Frontend

A344030 Composite numbers with distinct prime factors {p1, p2, ..., pk} in ascending order where p1^1 + p2^2 + ...+ pk^k is prime.

%I A344030 #11 Apr 09 2024 14:15:49
%S A344030 4,6,8,9,12,16,18,24,25,27,32,36,48,49,54,64,72,81,96,108,121,125,128,
%T A344030 144,162,169,192,216,243,256,288,289,324,343,361,384,390,399,432,455,
%U A344030 465,486,512,529,570,576,595,625,627,648,690,729,768,780,841,864,903
%N A344030 Composite numbers with distinct prime factors {p1, p2, ..., pk} in ascending order where p1^1 + p2^2 + ...+ pk^k is prime.
%H A344030 Robert Israel, <a href="/A344030/b344030.txt">Table of n, a(n) for n = 1..10000</a>
%e A344030 24 has distinct prime factors {2, 3} and 2^1 + 3^2 = 11 is prime.
%e A344030 570 has distinct prime factors {2, 3, 5, 19} and 2^1 + 3^2 + 5^3 + 19^4 = 130457 is prime.
%p A344030 filter:= proc(n) local F,i;
%p A344030   if isprime(n) then return false fi;
%p A344030   F:= sort(convert(numtheory:-factorset(n),list));
%p A344030   isprime(add(F[i]^i,i=1..nops(F)))
%p A344030 end proc:
%p A344030 select(filter, [$4..1000]); # _Robert Israel_, Apr 09 2024
%t A344030 Select[Range@1000,!PrimeQ@#&&PrimeQ@Total[(a=First/@FactorInteger[#])^Range@Length[a]]&]
%o A344030 (PARI) isok(c) = if (!isprime(c), my(f=factor(c)); isprime(sum(k=1, #f~, f[k,1]^k))); \\ _Michel Marcus_, May 07 2021
%Y A344030 Cf. A027748, A343300.
%K A344030 nonn
%O A344030 1,1
%A A344030 _Giorgos Kalogeropoulos_, May 07 2021