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

1,1

Links

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

Example

315 is a term because 315' = 318 and 318 - 315 = 3 is prime.

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);

Prog

(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
(PARI) lista(c, k=0)= vector(c, i, my(f, p); until(isprime(p), f=factor(k++)~; p=k*sum(j=1, #f, f[2, j]/f[1, j])-k); k); \\ Ruud H.G. van Tol, Dec 04 2025

Crossrefs

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

Sequence in context: A304202 A298988 A025959 * A261484 A004323 A025937

Adjacent sequences: A229267 A229268 A229269 * A229271 A229272 A229273

Keyword

nonn

Author

Paolo P. Lava, Sep 18 2013

Status

approved