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

1,1

Links

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

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 *)

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 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

Crossrefs

Cf. A025473, A025475, A048148, A246547.

Sequence in context: A157987 A025478 A084371 * A347731 A331532 A078773

Adjacent sequences: A025473 A025474 A025475 * A025477 A025478 A025479

Keyword

easy,nonn

Author

David W. Wilson

Status

approved