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A368715
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Numbers that are not coprime to the maximal exponent in their prime factorization.
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3
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4, 12, 16, 18, 20, 24, 27, 28, 36, 44, 48, 50, 52, 54, 60, 64, 68, 72, 76, 80, 84, 90, 92, 98, 100, 108, 112, 116, 120, 124, 126, 132, 135, 140, 144, 148, 150, 156, 160, 162, 164, 168, 172, 176, 180, 188, 189, 192, 196, 198, 204, 208, 212, 216, 220, 228, 234, 236, 240, 242, 244
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OFFSET
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1,1
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COMMENTS
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Subsequence of A137257 and first differs from it at n = 51.
Numbers k such that gcd(k, A051903(k)) > 1.
Includes all the nonsquarefree terms of A336064.
The asymptotic density of this sequence is 1 - 1/zeta(2) - Sum_{k>=2} (1/(f(k+1, k) * zeta(k+1)) - 1/(f(k, k) * zeta(k))) = 0.24998449199080279703..., where f(e, m) = Product_{primes p|m} ((1-1/p^e)/(1-1/p)).
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LINKS
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MATHEMATICA
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Select[Range[210], !CoprimeQ[#, Max[FactorInteger[#][[;; , 2]]]] &]
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PROG
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(PARI) lista(kmax) = for(k = 2, kmax, if(gcd(k, vecmax(factor(k)[, 2])) > 1, print1(k, ", ")));
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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