A390188 - OEIS

%I #18 Oct 30 2025 04:39:56

%S 125,243,343,1331,2187,2197,4913,6859,12167,16807,24389,29791,50653,

%T 68921,78125,79507,103823,148877,161051,177147,205379,226981,300763,

%U 357911,371293,389017,493039,571787,704969,912673,1030301,1092727,1225043,1295029,1419857,1442897

%N Numbers of the form p^q with odd primes p != q.

%H Michael De Vlieger, <a href="/A390188/b390188.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 10^7: # for terms <= N

%p P:= select(isprime, {seq(i,i=3..floor(N^(1/3)),2)}):

%p sort(select(`<=`,[seq(seq(p^q, q = P minus {p}),p = P)],N)); # _Robert Israel_, Oct 29 2025

%t 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 *)

%o (Python)

%o from sympy import primepi, integer_nthroot, primerange

%o from oeis_sequences.OEISsequences import bisection

%o def A390188(n):

%o     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())))

%o     return bisection(f,n,n) # _Chai Wah Wu_, Oct 29 2025

%Y Subsequence of A118092.

%Y Cf. A390179.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Oct 29 2025