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
Keywords
Programs
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Maple
select(n -> isprime(A367175(n)), [seq(1..10000)]);
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Mathematica
Select[Range[10000], And[# > 1, PrimeQ[#]] &@ DivisorSum[#, (-1)^Boole[PrimeQ[#]]*# &] &] (* Michael De Vlieger, Nov 10 2023 *)
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PARI
isok(k) = isprime(sumdiv(k, d, (-1)^isprime(d)*d)); \\ Michel Marcus, Nov 10 2023
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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
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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)])
Formula
k is a term if and only if A367175(k) is prime.