cp's OEIS Frontend

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

%I A229270 #15 Jul 29 2025 08:38:48
%S A229270 18,210,315,330,390,462,510,546,690,726,798,870,930,966,1110,1218,
%T A229270 1230,1290,1302,1554,1590,1770,2010,2130,2190,2310,2370,2490,2730,
%U A229270 2910,3030,3210,3270,3570,3810,4110,4290,4470,4530,4830,4890,5010,5430,5790,5910,5970
%N A229270 Numbers k for which k' - k is prime, k' being the arithmetic derivative of k.
%H A229270 Paolo P. Lava, <a href="/A229270/b229270.txt">Table of n, a(n) for n = 1..500</a>
%e A229270 315 is in the list because 315’ = 318 and 318 - 315 = 3 that is prime.
%p A229270 with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do
%p A229270 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 A229270 (Python)
%o A229270 from sympy import isprime, factorint
%o A229270 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 A229270 Cf. A003415, A165561, A165562, A229269, A229271, A229272.
%K A229270 nonn
%O A229270 1,1
%A A229270 _Paolo P. Lava_, Sep 18 2013