A394061 - OEIS

%I #21 Mar 19 2026 21:42:23

%S 2,7,5,5,7,5,5,13,5,7,5,7,5,5,5,13,7,17,5,13,73,5,7,5,23,23,31,139,29,

%T 5,17,5,43,13,193,23,17,29,5,61,5,17,19,47,73,53,5,43,349,29,31,5,17,

%U 5,17,53,433,5,41,71,463,17,7,43,47,37,17,29,139,29,19,89,53,17,23,41,13

%N Prime number produced by summing the distinct prime factors of the numbers in A393096.

%F a(n) = A008472 (A393096(n)).

%e For n = 8, a(8) is 13, the sum of 2 and 11 which are the distinct prime factors of 44, given by a(8) in A393096.

%t sopf[k_]:=Total[First/@FactorInteger[k]];q[k_]:=PrimeQ[sopf[k]]&&PrimeQ[k-sopf[k]];sopf/@Select[Range[2850],q] (* _James C. McMahon_, Mar 16 2026 *)

%o (Python)

%o from sympy import isprime, primefactors

%o def ok(n):return isprime(sum(primefactors(n))) and isprime(n-sum(primefactors(n)))

%o print(list(map(lambda n: sum(primefactors(n)), filter(ok, range(1, 2000)))))

%o (PARI) sopf(k) = vecsum(factor(k)[,1]);

%o isok(k) = my(s=sopf(k)); isprime(s) && isprime(k-s);

%o apply(sopf, select(isok, [1..4000])) \\ _Michel Marcus_, Mar 09 2026

%Y Cf. A008472, A393096.

%K nonn

%O 1,1

%A _Guy Siviour_, Mar 09 2026