OFFSET
1,1
COMMENTS
The only prime in this sequence is 2. Since it is the only even prime and p' = 1, it is the only prime that added to its derivative can give an odd prime (namely 3).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
EXAMPLE
46 is in the list because: n=46 -> n'=25 -> n+n'=71 that is prime.
MAPLE
with(numtheory);
P:= proc(n)
local a, i, p, pfs;
for i from 1 to n do
pfs:=ifactors(i)[2]; a:=i*add(op(2, p)/op(1, p), p=pfs);
if isprime(a+i) then print(i); fi;
od;
end:
P(1000);
# alternative
isA165562 := proc(n)
isprime(A129283(n)) ;
end proc:
for n from 1 to 1000 do
if isA165562(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Feb 04 2022
MATHEMATICA
PROG
(Python)
from sympy import isprime, factorint
A165562 = [n for n in range(1, 10**5) if isprime(n+sum([int(n*e/p) for p, e in factorint(n).items()]))] # Chai Wah Wu, Aug 21 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paolo P. Lava and Giorgio Balzarotti, Sep 25 2009
EXTENSIONS
Terms verified by Alonso del Arte, Oct 30 2009
STATUS
approved