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 A076470 Perfect powers m^k where k >= 6. 6
 1, 64, 128, 256, 512, 729, 1024, 2048, 2187, 4096, 6561, 8192, 15625, 16384, 19683, 32768, 46656, 59049, 65536, 78125, 117649, 131072, 177147, 262144, 279936, 390625, 524288, 531441, 823543, 1000000, 1048576, 1594323, 1679616, 1771561 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A necessary but not sufficient condition is that if p|n when at least p^6|n. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA Sum_{n>=1} 1/a(n) = 5 - zeta(2) - zeta(3) - zeta(4) - zeta(5) + Sum_{k>=2} mu(k)*(5 - zeta(k) - zeta(2*k) - zeta(3*k) - zeta(4*k) - zeta(5*k)) = 1.03342597171... . - Amiram Eldar, Dec 03 2022 MATHEMATICA a = {1}; Do[ If[ Apply[ GCD, Last[ Transpose[ FactorInteger[n]]]] > 4, a = Append[a, n]; Print[n]], {n, 2, 1953124}]; a PROG (Python) from sympy import mobius, integer_nthroot def A076470(n): def f(x): return int(n+9+x-(sum(integer_nthroot(x, d)[0] for d in (6, 10, 15))<<1)-sum(integer_nthroot(x, d)[0] for d in (8, 9, 12, 20, 25))+sum(mobius(k)*(sum(integer_nthroot(x, k*i)[0] for i in range(1, 6))-5) for k in range(6, 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 kmax # Chai Wah Wu, Aug 14 2024 CROSSREFS Cf. A001597, A076467, A076468, A076469. Different from A069493. Cf. A002117, A013661, A013662, A013663. Sequence in context: A023708 A172420 A069493 * A256820 A031464 A045076 Adjacent sequences: A076467 A076468 A076469 * A076471 A076472 A076473 KEYWORD nonn AUTHOR Robert G. Wilson v, Oct 14 2002 STATUS approved

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Last modified September 15 08:55 EDT 2024. Contains 375932 sequences. (Running on oeis4.)