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A335275
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Numbers k such that the largest square dividing k is a unitary divisor of k.
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14
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1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76
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OFFSET
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1,2
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COMMENTS
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Numbers whose prime factorization contains exponents that are either 1 or even.
Numbers whose powerful part (A057521) is a square.
First differs from A220218 at n = 227: a(227) = 256 is not a term of A220218.
The asymptotic density of this sequence is Product_{p prime} (1 - 1/(p^2*(p+1))) = 0.881513... (A065465).
Differs from A096432 in having or not having 1, 256, 432, 648, 768, 1280, 1728, 1792, 2000, 2160, 2304,... - R. J. Mathar, Jul 22 2020
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LINKS
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EXAMPLE
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12 is a term since the largest square dividing 12 is 4, and 4 and 12/4 = 3 are coprime.
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MATHEMATICA
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seqQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # == 1 || EvenQ[#] &]; Select[Range[100], seqQ]
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PROG
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(PARI) isok(k) = my(d=k/core(k)); gcd(d, k/d) == 1; \\ Michel Marcus, Jul 07 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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