A229270 Numbers k for which k' - k is prime, k' being the arithmetic derivative of k.

18, 210, 315, 330, 390, 462, 510, 546, 690, 726, 798, 870, 930, 966, 1110, 1218, 1230, 1290, 1302, 1554, 1590, 1770, 2010, 2130, 2190, 2310, 2370, 2490, 2730, 2910, 3030, 3210, 3270, 3570, 3810, 4110, 4290, 4470, 4530, 4830, 4890, 5010, 5430, 5790, 5910, 5970

Offset: 1

Author

Paolo P. Lava, Sep 18 2013

Keywords

• nonn

Examples

			315 is in the list because 315’ = 318 and 318 - 315 = 3 that is prime.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A003415, A165561, A165562, A229269, A229271, A229272.

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) then print(n); fi; od; end: P(10^5);

Python

from sympy import isprime, factorint
A229270 = [n for n in range(1,10**5) if isprime(sum([int(n*e/p) for p,e in factorint(n).items()])-n)] # Chai Wah Wu, Aug 21 2014