This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A052128 #26 Jul 02 2025 16:01:58
%S A052128 1,1,1,1,1,2,1,1,1,2,1,3,1,2,3,1,1,2,1,4,3,2,1,3,1,2,1,4,1,5,1,1,3,2,
%T A052128 5,4,1,2,3,5,1,6,1,4,5,2,1,3,1,2,3,4,1,2,5,7,3,2,1,5,1,2,7,1,5,6,1,4,
%U A052128 3,7,1,8,1,2,3,4,7,6,1,5,1,2,1,7,5,2,3,8,1,9,7,4,3,2,5,3,1,2,9,4,1,6
%N A052128 a(1) = 1; for n > 1, a(n) is the largest divisor of n that is coprime to a larger divisor of n.
%C A052128 Least k > 0 such that the resultant of the k-th cyclotomic polynomial and the n-th cyclotomic polynomial is not 1. - _Benoit Cloitre_, Oct 13 2002
%C A052128 From _Jianing Song_, Sep 28 2022: (Start)
%C A052128 a(n) is the largest divisor d of n such that d <= sqrt(n) and that gcd(d,n/d) = 1.
%C A052128 Proof: write n = Product_{1<=i<=r} (p_i)^(e_i), let d be the largest divisor of n such that d <= sqrt(n) and that gcd(d,n/d) = 1. Obviously we have a(n) >= d. Suppose that a(n) = Product_{1<=i<=s} (p_i)^(m_i) for s <= r, 1 <= m_i <= e_i, then the larger divisor to which a(n) is coprime is a divisor of Product_{s+1<=i<=r} (p_i)^(e_i), so by definition we have a(n) <= min{Product_{1<=i<=s} (p_i)^(e_i), Product_{s+1<=i<=r} (p_i)^(e_i)} <= d. Thus a(n) = d. (End)
%H A052128 Charles R Greathouse IV, <a href="/A052128/b052128.txt">Table of n, a(n) for n = 1..10000</a>
%F A052128 a(n) = n / A354933(n) = A354933(n) - A076388(n). - _Antti Karttunen_, Jun 16 2022
%e A052128 a(6) = 6 / 3^1 = 2.
%t A052128 Table[best = 1; d = Divisors[n]; While[Length[d] > 1, e = d[[1]]; d = Rest[d]; If[Min[GCD[e, d]] == 1, best = e]]; best, {n, 102}] (* _T. D. Noe_, Aug 23 2013 *)
%o A052128 (PARI) a(n) = my(i, j, d = divisors(n)); forstep (i = #d-1, 1, -1, for (j = i+1, #d, if (gcd(d[i], d[j]) == 1, return (d[i])))); 1 \\ _Michel Marcus_, Aug 22 2013
%o A052128 (PARI) a(n)=my(f=factor(n),v=[1]); for(i=1,#f~,v=concat(v, f[i,1]^f[i,2] *v)); v=vecsort(v); forstep(i=#v\2,2,-1,for(j=i+1,#v-1, if(gcd(v[i],v[j])==1,return(v[i])))); 1 \\ _Charles R Greathouse IV_, Aug 22 2013
%o A052128 (PARI) A052128(n) = fordiv(n,d,if((d>=(n/d)) && 1==gcd(d,n/d), return(n/d))); \\ _Antti Karttunen_, Jun 16 2022
%Y A052128 Cf. A054372, A076388, A354933.
%K A052128 nonn
%O A052128 1,6
%A A052128 _James Sellers_, Jan 21 2000
%E A052128 Terms corrected by _Charles R Greathouse IV_, Aug 22 2013
%E A052128 Definition rewritten by _Jianing Song_, Sep 28 2022