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A229270
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Numbers n for which n’-n is prime, n' being the arithmetic derivative of n.
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4
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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315 is in the list because 315’ = 318 and 318 - 315 = 3 that is prime.
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MAPLE
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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);
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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