cp's OEIS Frontend

A145521 Take the primes raised to prime exponents, arranged in numerical order (A053810). If A053810(n) = r(n)^q(n), where r(n) and q(n) are primes, then a(n) = q(n)^r(n).

%I A145521 #14 Aug 14 2024 01:51:13
%S A145521 4,9,8,32,27,25,128,2048,243,49,8192,125,131072,2187,524288,8388608,
%T A145521 536870912,2147483648,177147,137438953472,2199023255552,8796093022208,
%U A145521 121,343,1594323,140737488355328,9007199254740992,3125,576460752303423488,2305843009213693952,147573952589676412928
%N A145521 Take the primes raised to prime exponents, arranged in numerical order (A053810). If A053810(n) = r(n)^q(n), where r(n) and q(n) are primes, then a(n) = q(n)^r(n).
%C A145521 a(n) = A053812(n)^A053811(n).
%o A145521 (PARI) lista(nn) = for(k=1, nn, if(isprime(isprimepower(k, &p)), print1(bigomega(k)^p, ", "))); \\ _Jinyuan Wang_, Feb 25 2020
%o A145521 (Python)
%o A145521 from math import prod
%o A145521 from sympy import primepi, integer_nthroot, primerange, factorint
%o A145521 def A145521(n):
%o A145521     def f(x): return int(n-1+x-sum(primepi(integer_nthroot(x, p)[0]) for p in primerange(x.bit_length())))
%o A145521     kmin, kmax = 1,2
%o A145521     while f(kmax) >= kmax:
%o A145521         kmax <<= 1
%o A145521     while True:
%o A145521         kmid = kmax+kmin>>1
%o A145521         if f(kmid) < kmid:
%o A145521             kmax = kmid
%o A145521         else:
%o A145521             kmin = kmid
%o A145521         if kmax-kmin <= 1:
%o A145521             break
%o A145521     return prod(e**p for p,e in factorint(kmax).items()) # _Chai Wah Wu_, Aug 13 2024
%Y A145521 Cf. A053810, A053811, A053812, A145522.
%K A145521 nonn
%O A145521 1,1
%A A145521 _Leroy Quet_, Oct 12 2008
%E A145521 Extended by _Ray Chandler_, Nov 01 2008
%E A145521 More terms from _Jinyuan Wang_, Feb 25 2020