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Numbers n for which nā€™-n is prime, n' being the arithmetic derivative of n.
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%I #9 Aug 25 2014 03:49:29

%S 18,210,315,330,390,462,510,546,690,726,798,870,930,966,1110,1218,

%T 1230,1290,1302,1554,1590,1770,2010,2130,2190,2310,2370,2490,2730,

%U 2910,3030,3210,3270,3570,3810,4110,4290,4470,4530,4830,4890,5010,5430,5790,5910,5970

%N Numbers n for which nā€™-n is prime, n' being the arithmetic derivative of n.

%H Paolo P. Lava, <a href="/A229270/b229270.txt">Table of n, a(n) for n = 1..500</a>

%e 315 is in the list because 315ā€™ = 318 and 318 - 315 = 3 that is prime.

%p with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do

%p 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);

%o (Python)

%o from sympy import isprime, factorint

%o 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

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

%K nonn

%O 1,1

%A _Paolo P. Lava_, Sep 18 2013