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a(1)=1. a(n) = smallest positive integer not occurring among the first n-1 terms of the sequence that is coprime to n and is coprime to every (nonzero) exponent in the prime factorization of n.

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`%I #11 Aug 27 2022 04:09:40
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`%S 1,3,2,5,4,7,6,11,13,9,8,17,10,15,14,19,12,23,16,21,20,25,18,29,27,31,
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`%T 22,33,24,37,26,39,28,35,32,41,30,43,34,47,36,53,38,45,49,51,40,55,57,
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`%U 59,44,61,42,65,46,67,50,63,48,71,52,69,73,77,54,79,56,75,58,81,60,83
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`%N a(1)=1. a(n) = smallest positive integer not occurring among the first n-1 terms of the sequence that is coprime to n and is coprime to every (nonzero) exponent in the prime factorization of n.
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`%e 12 has the prime-factorization of 2^2 * 3^1. The positive integers that don't occur among the first 11 terms of the sequence are 10,12,14,15,16,17,18,19,... Of these integers, 17 is the smallest that is coprime to the exponents in the prime factorization of 12 (i.e., coprime to 2 and 1) and is coprime to 12. So a(12) = 17.
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`%Y Cf. A138308, A138311.
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`%K nonn
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`%O 1,2
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`%A _Leroy Quet_, Mar 13 2008
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`%E More terms from _Max Alekseyev_, Apr 24 2010
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