|
|
A025476
|
|
Prime root of n-th nontrivial prime power (A025475, A246547).
|
|
5
|
|
|
2, 2, 3, 2, 5, 3, 2, 7, 2, 3, 11, 5, 2, 13, 3, 2, 17, 7, 19, 2, 23, 5, 3, 29, 31, 2, 11, 37, 41, 43, 2, 3, 13, 47, 7, 53, 5, 59, 61, 2, 67, 17, 71, 73, 79, 3, 19, 83, 89, 2, 97, 101, 103, 107, 109, 23, 113, 11, 5, 127, 2, 7, 131, 137, 139, 3, 149, 151, 29, 157, 163, 167, 13, 31, 173, 179
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
MAPLE
|
cvm := proc(n, level) local f, opf; if n < 2 then RETURN() fi;
f := ifactors(n); opf := op(1, op(2, f)); if nops(op(2, f)) > 1 or
op(2, opf) <= level then RETURN() fi; op(1, opf) end:
A025476_list := n -> seq(cvm(i, 1), i=1..n); # n is search limit
# Alternative:
isA246547 := n -> n > 1 and not isprime(n) and type(n, 'primepower'):
seq(ifactors(p)[2][1][1], p in select(isA246547, [$1..30000])); # Peter Luschny, Jul 15 2023
|
|
MATHEMATICA
|
Transpose[ Flatten[ FactorInteger[ Select[ Range[2, 30000], !PrimeQ[ # ] && Mod[ #, # - EulerPhi[ # ]] == 0 &]], 1]][[1]] (* Robert G. Wilson v *)
|
|
PROG
|
(PARI) forcomposite(n=4, 10^5, if( ispower(n, , &p) && isprime(p), print1(p, ", "))) \\ Joerg Arndt, Sep 11 2021
(Python)
from sympy import primepi, integer_nthroot, primefactors
def f(x): return int(n-1+x-sum(primepi(integer_nthroot(x, k)[0]) for k in range(2, x.bit_length())))
kmin, kmax = 1, 2
while f(kmax) >= kmax:
kmax <<= 1
while True:
kmid = kmax+kmin>>1
if f(kmid) < kmid:
kmax = kmid
else:
kmin = kmid
if kmax-kmin <= 1:
break
return primefactors(kmax)[0] # Chai Wah Wu, Aug 15 2024
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,changed
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|