A396547 Primes p such that the sum of the distinct prime factors of p-1 is prime.

3, 5, 7, 11, 13, 17, 19, 23, 37, 41, 59, 73, 83, 89, 97, 101, 109, 137, 163, 193, 211, 233, 251, 257, 353, 359, 383, 401, 421, 433, 463, 479, 487, 563, 569, 571, 577, 631, 641, 769, 809, 839, 857, 859, 863, 929, 1051, 1097, 1153, 1171, 1193, 1283, 1291, 1297, 1303, 1319, 1409, 1429, 1433, 1459

Offset

1,1

Links

Vincenzo Manto, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(n) isprime(n) and isprime(convert(NumberTheory:-PrimeFactors(n-1), `+`)) end proc:
select(filter, [seq(i, i=3..2000)]); # Robert Israel, May 29 2026

Mathematica

Select[Prime[Range[300]], PrimeQ[Total[FactorInteger[# - 1][[All, 1]]]] &]

Prog

(Python)
from sympy import isprime, primerange, primefactors
def sequence(limit):
    res = []
    for p in primerange(2, limit):
        if isprime(sum(primefactors(p - 1))):
            res.append(p)
    return res
print(sequence(2000))

Crossrefs

Cf. A008472, A023507.

Sequence in context: A000978 A128925 A204142 * A131261 A100276 A225669

Adjacent sequences: A396544 A396545 A396546 * A396548 A396549 A396550

Keyword

nonn

Author

Vincenzo Manto, May 28 2026

Status

approved