A229272 Numbers n for which n' + n and n' - n are both prime, n' being the arithmetic derivative of n.

210, 330, 390, 690, 798, 966, 1110, 1230, 2190, 2310, 2730, 3270, 4110, 4530, 4890, 5430, 6090, 6270, 6810, 6990, 7230, 7890, 8310, 8490, 9030, 9210, 9282, 10470, 10590, 10770, 12090, 12210, 12270, 12570, 12810, 12930, 13110, 13830, 14070, 17070, 17094, 17310

Offset: 1

Author

Paolo P. Lava, Sep 18 2013

Keywords

• nonn

Comments

Intersection of A165561 and A229270.

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A003415, A165561, A165562, A229269-A229271.

Programs

Maple

with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do
a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
if isprime(a+n) and isprime(a-n) then print(n); fi;
od; end: P(10^5);

Python

from sympy import isprime, factorint
A229272 = []
for n in range(1, 10**5):
    np = sum([int(n*e/p) for p, e in factorint(n).items()]) if n > 1 else 0
    if isprime(np+n) and isprime(np-n):
        A229272.append(n)
# Chai Wah Wu, Aug 21 2014