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A056196
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Numbers n such that A055229(n) = 2.
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2
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8, 24, 32, 40, 56, 72, 88, 96, 104, 120, 128, 136, 152, 160, 168, 184, 200, 224, 232, 248, 264, 280, 288, 296, 312, 328, 344, 352, 360, 376, 384, 392, 408, 416, 424, 440, 456, 472, 480, 488, 504, 512, 520, 536, 544, 552, 568, 584, 600, 608, 616, 632, 640
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OFFSET
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1,1
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COMMENTS
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By definition, the largest square divisor and squarefree part of these numbers have GCD = 2.
Numbers of the form 2^(2*k+1) * m, where k >= 1 and m is an odd number whose prime factorization contains only exponents that are either 1 or even. The asymptotic density of this sequence is (1/12) * Product_{p odd prime} (1-1/(p^2*(p+1))) = A065465 / 11 = 0.08013762179319734335... - Amiram Eldar, Dec 04 2020, Nov 25 2022
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LINKS
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EXAMPLE
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88 is here because 88 has squarefree part 22, largest square divisor 4, and A055229(88) = gcd(22, 4) = 2.
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MAPLE
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filter:= proc(n) local T;
T:= select(t -> (t[2]::odd and t[2]>1), ifactors(n)[2]);
nops(T) = 1 and T[1][1]=2;
end proc:
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MATHEMATICA
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PROG
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(PARI) isok(n) = my(c=core(n)); gcd(c, n/c) == 2; \\ after PARI in A055229; Michel Marcus, Sep 20 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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