A394061 Prime number produced by summing the distinct prime factors of the numbers in A393096.

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, 5, 17, 5, 43, 13, 193, 23, 17, 29, 5, 61, 5, 17, 19, 47, 73, 53, 5, 43, 349, 29, 31, 5, 17, 5, 17, 53, 433, 5, 41, 71, 463, 17, 7, 43, 47, 37, 17, 29, 139, 29, 19, 89, 53, 17, 23, 41, 13

Offset

1,1

Links

Table of n, a(n) for n=1..77.

Formula

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

Example

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.

Mathematica

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 *)

Prog

(Python)
from sympy import isprime, primefactors
def ok(n):return isprime(sum(primefactors(n))) and isprime(n-sum(primefactors(n)))
print(list(map(lambda n: sum(primefactors(n)), filter(ok, range(1, 2000)))))
(PARI) sopf(k) = vecsum(factor(k)[, 1]);
isok(k) = my(s=sopf(k)); isprime(s) && isprime(k-s);
apply(sopf, select(isok, [1..4000])) \\ Michel Marcus, Mar 09 2026

Crossrefs

Cf. A008472, A393096.

Sequence in context: A119929 A195070 A352619 * A151856 A248223 A019825

Adjacent sequences: A394058 A394059 A394060 * A394062 A394063 A394064

Keyword

nonn

Author

Guy Siviour, Mar 09 2026

Status

approved