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 A059404 Numbers with different exponents in their prime factorizations. 27
 12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 80, 84, 88, 90, 92, 96, 98, 99, 104, 108, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Former name: Numbers k such that k/(largest power of squarefree kernel of k) is larger than 1. Complement of A072774 (powers of squarefree numbers). Also numbers k = p(1)^alpha(1)* ... * p(r)^alpha(r) such that RootMeanSquare(alpha(1), ..., alpha(r)) is not an integer. - Ctibor O. Zizka, Sep 19 2008 LINKS Donald Alan Morrison, Table of n, a(n) for n = 1..10000 Donald Alan Morrison, Sage program FORMULA A062760(a(n)) > 1, i.e., a(n)/(A007947(a(n))^A051904(a(n)) = a(n)/A062759(n) > 1. A071625(a(n)) > 1. - Michael S. Branicky, Sep 01 2022 EXAMPLE 440 is in the sequence because 440 = 2^3*5*11 and it has two distinct exponents, 3 and 1. PROG (PARI) is(n)=#Set(factor(n)[, 2])>1 \\ Charles R Greathouse IV, Sep 18 2015 (Python) from sympy import factorint def ok(n): return len(set(factorint(n).values())) > 1 print([k for k in range(190) if ok(k)]) # Michael S. Branicky, Sep 01 2022 CROSSREFS Cf. A003557, A007947, A051904, A062759, A062760, A071625. Sequence in context: A317711 A359890 A323055 * A303946 A360246 A242416 Adjacent sequences: A059401 A059402 A059403 * A059405 A059406 A059407 KEYWORD nonn,easy AUTHOR Labos Elemer, Jul 18 2001 STATUS approved

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Last modified March 31 15:10 EDT 2023. Contains 361668 sequences. (Running on oeis4.)