A344030 - OEIS

%I #11 Apr 09 2024 14:15:49

%S 4,6,8,9,12,16,18,24,25,27,32,36,48,49,54,64,72,81,96,108,121,125,128,

%T 144,162,169,192,216,243,256,288,289,324,343,361,384,390,399,432,455,

%U 465,486,512,529,570,576,595,625,627,648,690,729,768,780,841,864,903

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

%H Robert Israel, <a href="/A344030/b344030.txt">Table of n, a(n) for n = 1..10000</a>

%e 24 has distinct prime factors {2, 3} and 2^1 + 3^2 = 11 is prime.

%e 570 has distinct prime factors {2, 3, 5, 19} and 2^1 + 3^2 + 5^3 + 19^4 = 130457 is prime.

%p filter:= proc(n) local F,i;

%p   if isprime(n) then return false fi;

%p   F:= sort(convert(numtheory:-factorset(n),list));

%p   isprime(add(F[i]^i,i=1..nops(F)))

%p end proc:

%p select(filter, [$4..1000]); # _Robert Israel_, Apr 09 2024

%t Select[Range@1000,!PrimeQ@#&&PrimeQ@Total[(a=First/@FactorInteger[#])^Range@Length[a]]&]

%o (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 Cf. A027748, A343300.

%K nonn

%O 1,1

%A _Giorgos Kalogeropoulos_, May 07 2021