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A072414
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Non-Achilles numbers for which LCM of the exponents in the prime factorization of n is not equal to the maximum of the same exponents.
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5
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360, 504, 540, 600, 756, 792, 936, 1176, 1188, 1224, 1350, 1368, 1400, 1404, 1440, 1500, 1656, 1836, 1960, 2016, 2052, 2088, 2160, 2200, 2232, 2250, 2400, 2484, 2520, 2600, 2646, 2664, 2904, 2952, 3024, 3096, 3132, 3168, 3240, 3348, 3384, 3400, 3500
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OFFSET
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1,1
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COMMENTS
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Most members of this sequence fail to be Achilles numbers because they have at least one prime factor with multiplicity 1. There are also numbers in the sequence that fail to be Achilles numbers because they are perfect powers: these are precisely the proper powers of members of A072412, so the smallest such is 5184 = 2^6*3^4 = 72^2. - Franklin T. Adams-Watters, Oct 09 2006
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 1..10000
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FORMULA
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A051903(a(n)) is not equal A072411(a(n)) but the numbers are not in A052486.
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EXAMPLE
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m = 504 = 2*2*2*3*3*7: exponent-set = E = {3,2,1}, max(E) = 3 < lcm(E) = 6, gcd{E) = min(E) = 1.
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MATHEMATICA
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Select[Range@ 3500, And[LCM @@ # != Max@ #, GCD @@ # == Min@ # == 1] &[FactorInteger[#][[All, -1]] ] &] (* Michael De Vlieger, Jul 18 2017 *)
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PROG
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(PARI) is(n)=my(f=factor(n)[, 2]); n>9 && lcm(f)!=vecmax(f) && (#f==1 || vecmin(f)<2) \\ Charles R Greathouse IV, Oct 16 2015
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CROSSREFS
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Cf. A005361, A051903, A051904, A052409, A072411, A072412, A052486.
Sequence in context: A069478 A060665 A323024 * A163569 A063067 A076205
Adjacent sequences: A072411 A072412 A072413 * A072415 A072416 A072417
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Jun 17 2002
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STATUS
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approved
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