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A354933 a(1) = 1; for n > 1, a(n) = n / the largest divisor of n that is coprime to a larger divisor of n.

%I A354933 #13 Sep 28 2022 10:45:23
%S A354933 1,2,3,4,5,3,7,8,9,5,11,4,13,7,5,16,17,9,19,5,7,11,23,8,25,13,27,7,29,
%T A354933 6,31,32,11,17,7,9,37,19,13,8,41,7,43,11,9,23,47,16,49,25,17,13,53,27,
%U A354933 11,8,19,29,59,12,61,31,9,64,13,11,67,17,23,10,71,9,73,37,25,19,11,13,79,16,81,41,83,12,17,43
%N A354933 a(1) = 1; for n > 1, a(n) = n / the largest divisor of n that is coprime to a larger divisor of n.
%C A354933 a(n) is the smallest divisor d of n such that d >= sqrt(n) and that gcd(d,n/d) = 1. For the proof see A052128. - _Jianing Song_, Sep 28 2022
%H A354933 Antti Karttunen, <a href="/A354933/b354933.txt">Table of n, a(n) for n = 1..20000</a>
%F A354933 a(n) = n / A052128(n).
%F A354933 a(n) = A052128(n) + A076388(n).
%t A354933 a[n_] := SelectFirst[Divisors[n], # >= n/# && CoprimeQ[#, n/#] &]; Array[a, 100] (* _Amiram Eldar_, Jun 16 2022 *)
%o A354933 (PARI) A354933(n) = fordiv(n,d,if((d>=(n/d)) && 1==gcd(d,n/d), return(d)));
%Y A354933 Cf. A052128, A076388.
%Y A354933 Differs from A346596 for the first time at n=60, where a(60) = 12, while A346596(60) = 15.
%K A354933 nonn
%O A354933 1,2
%A A354933 _Antti Karttunen_, Jun 16 2022
%E A354933 Definition rewritten by _Jianing Song_, Sep 28 2022