Vincenzo Manto

A396547

Created: 6/3/2026 | Author: Vincenzo Manto , May 28 2026

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

Sequence Chart

Graph of A396547

Data

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

Computational Implementations

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))

Mathematica

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

Cross-References

See also OEIS entries: Cf. A008472, A023507.