A367176 Numbers k, such that (Sum_{d|k} (-1)^[d is prime] * d) is prime.

4, 6, 8, 9, 18, 32, 49, 50, 128, 162, 169, 242, 288, 400, 512, 578, 729, 900, 1058, 1156, 1521, 1600, 1682, 2048, 2116, 2312, 2450, 3025, 3249, 3600, 3872, 4356, 4418, 4489, 4624, 5000, 6241, 6728, 6962, 7225, 8100, 8281, 8450, 8464, 8649, 8712, 10000

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Formula

k is a term if and only if A367175(k) is prime.

Maple

select(n -> isprime(A367175(n)), [seq(1..10000)]);

Mathematica

Select[Range[10000], And[# > 1, PrimeQ[#]] &@ DivisorSum[#, (-1)^Boole[PrimeQ[#]]*# &] &] (* Michael De Vlieger, Nov 10 2023 *)

Prog

(SageMath)
def is_a(n): return is_prime(sum((-1)^is_prime(d)*d for d in divisors(n)))
print([n for n in range(1, 10001) if is_a(n)])
(PARI) isok(k) = isprime(sumdiv(k, d, (-1)^isprime(d)*d)); \\ Michel Marcus, Nov 10 2023
(Python)
from itertools import count, islice
from sympy import divisor_sigma, primefactors
def A367176_gen(startvalue=2): # generator of terms >= startvalue
    return filter(lambda n: isprime(divisor_sigma(n)-(sum(primefactors(n))<<1)), count(max(startvalue, 2)))
A367176_list = list(islice(A367176_gen(), 20)) # Chai Wah Wu, Nov 10 2023

Crossrefs

Cf. A367175, A023194, A114522.

Sequence in context: A123710 A075243 A024370 * A121719 A267509 A162738

Adjacent sequences: A367173 A367174 A367175 * A367177 A367178 A367179

Keyword

nonn

Author

Peter Luschny, Nov 10 2023

Status

approved