A025476 Prime root of n-th nontrivial prime power (A025475, A246547).

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

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025473, A025475, A048148, A246547.

Programs

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
A025476_list(30000);  # Peter Luschny, Sep 21 2011
# 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 *)

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 A025476(n):
    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