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 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). 2
 4, 9, 8, 32, 27, 25, 128, 2048, 243, 49, 8192, 125, 131072, 2187, 524288, 8388608, 536870912, 2147483648, 177147, 137438953472, 2199023255552, 8796093022208, 121, 343, 1594323, 140737488355328, 9007199254740992, 3125, 576460752303423488, 2305843009213693952, 147573952589676412928 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = A053812(n)^A053811(n). LINKS Table of n, a(n) for n=1..31. PROG (PARI) lista(nn) = for(k=1, nn, if(isprime(isprimepower(k, &p)), print1(bigomega(k)^p, ", "))); \\ Jinyuan Wang, Feb 25 2020 (Python) from math import prod from sympy import primepi, integer_nthroot, primerange, factorint def A145521(n): def f(x): return int(n-1+x-sum(primepi(integer_nthroot(x, p)[0]) for p in primerange(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 prod(e**p for p, e in factorint(kmax).items()) # Chai Wah Wu, Aug 13 2024 CROSSREFS Cf. A053810, A053811, A053812, A145522. Sequence in context: A297439 A168175 A164382 * A230979 A145431 A196516 Adjacent sequences: A145518 A145519 A145520 * A145522 A145523 A145524 KEYWORD nonn AUTHOR Leroy Quet, Oct 12 2008 EXTENSIONS Extended by Ray Chandler, Nov 01 2008 More terms from Jinyuan Wang, Feb 25 2020 STATUS approved

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Last modified September 13 03:33 EDT 2024. Contains 375857 sequences. (Running on oeis4.)