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 A233410 a(n) = smallest multiple m of n such that there are at most m/n perfect powers <= m. 1
 1, 2, 3, 20, 45, 60, 77, 96, 117, 180, 209, 276, 312, 378, 420, 464, 510, 594, 646, 700, 756, 814, 874, 936, 1050, 1118, 1188, 1260, 1363, 1440, 1519, 1632, 1716, 1836, 1925, 2016, 2183, 2394, 2496, 2600, 2788, 2898, 3010, 3124, 3330 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A perfect power is a power k^e with e != 1 (see A001597). No value of the sequence belongs to A001597 except the first value 1. LINKS Martin Y. Champel, Table of n, a(n) for n = 1..9999 New Scientist, Enigma 1777. Powerful tombola, by Susan Denham, November 2013. EXAMPLE n=1: a(1)=1 as the only perfect power <= 1 is 1. n=2: a(2)=2 as the only perfect power <= 2 is 1, and 2=2*1. n=3: a(3)=3 as the only perfect power <= 3 is 1, and 3=3*1. n=4: a(4)=20 as (1,4,8,9,16) are 5 perfect powers smaller than 20 and 20 = 4*5. n=5: a(5)=45 as (1,4,8,9,16,25,27,32,36) are 9 perfect powers smaller than 45 and 45 = 5*9. PROG (Python) # requires python code of A001597 class A233410() : def __init__(self) : self.a001597 = A001597() def perf_pows_up_to(self, n): idx = 1 while True: if self.a001597.at(idx) > n : return idx-1 idx += 1 def at(self, n): k = 1 while True : m = k*n if self.perf_pows_up_to(m) <= k: return m k += 1 a233410 = A233410() for n in range(1, 20): print(a233410.at(n)) # R. J. Mathar, Mar 29 2023 CROSSREFS Cf. A001597 = list of perfect powers, A069623 = number of perfect powers <= n Sequence in context: A191423 A195686 A295365 * A318765 A055814 A151370 Adjacent sequences: A233407 A233408 A233409 * A233411 A233412 A233413 KEYWORD nonn AUTHOR Martin Y. Champel, Dec 09 2013 STATUS approved

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Last modified June 7 04:39 EDT 2023. Contains 363151 sequences. (Running on oeis4.)