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A390188
Numbers of the form p^q with odd primes p != q.
4
125, 243, 343, 1331, 2187, 2197, 4913, 6859, 12167, 16807, 24389, 29791, 50653, 68921, 78125, 79507, 103823, 148877, 161051, 177147, 205379, 226981, 300763, 357911, 371293, 389017, 493039, 571787, 704969, 912673, 1030301, 1092727, 1225043, 1295029, 1419857, 1442897
OFFSET
1,1
LINKS
MAPLE
N:= 10^7: # for terms <= N
P:= select(isprime, {seq(i, i=3..floor(N^(1/3)), 2)}):
sort(select(`<=`, [seq(seq(p^q, q = P minus {p}), p = P)], N)); # Robert Israel, Oct 29 2025
MATHEMATICA
nn = 1500000; p = 3; Union@ Reap[While[q = 3; While[p^q < nn, If[p != q, Sow[p^q] ]; q = NextPrime[q]]; q > 3, p = NextPrime[p] ] ][[-1, 1]] (* Michael De Vlieger, Oct 29 2025 *)
PROG
(Python)
from sympy import primepi, integer_nthroot, primerange
from oeis_sequences.OEISsequences import bisection
def A390188(n):
def f(x): return int(n+x-sum(primepi(integer_nthroot(x, p)[0])-1-(x>=p**p) for p in primerange(3, x.bit_length())))
return bisection(f, n, n) # Chai Wah Wu, Oct 29 2025
CROSSREFS
Subsequence of A118092.
Cf. A390179.
Sequence in context: A038867 A378355 A029782 * A043351 A023724 A084647
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Oct 29 2025
STATUS
approved