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A284255 Largest divisor of n such that all its prime factors are less than the square of the smallest prime factor of n, a(1) = 1.

%I A284255 #25 Mar 28 2021 07:01:34
%S A284255 1,2,3,4,5,6,7,8,9,2,11,12,13,2,15,16,17,18,19,4,21,2,23,24,25,2,27,4,
%T A284255 29,6,31,32,3,2,35,36,37,2,3,8,41,6,43,4,45,2,47,48,49,2,3,4,53,54,55,
%U A284255 8,3,2,59,12,61,2,63,64,65,6,67,4,3,2,71,72,73,2,75,4,77,6,79,16,81,2,83,12,85,2,3,8,89,18,91,4,3,2,95,96,97,2,9,4,101,6
%N A284255 Largest divisor of n such that all its prime factors are less than the square of the smallest prime factor of n, a(1) = 1.
%H A284255 Antti Karttunen, <a href="/A284255/b284255.txt">Table of n, a(n) for n = 1..10001</a>
%F A284255 a(n) = n / A284254(n).
%F A284255 Other identities. For all n >= 1:
%F A284255 A006530(a(n)) = A284260(n).
%F A284255 A020639(a(n)) = A020639(n).
%F A284255 A001221(a(n)) = A284259(n).
%F A284255 A001222(a(n)) = A284257(n).
%e A284255 For n = 50 = 2*5*5, only prime less than 2^2 is 2, thus a(50) = 2.
%e A284255 For n = 90 = 2*3*3*5, the primes less than 2^2 are 2, 3 and 3, thus a(90) = 2*3*3 = 18.
%t A284255 Table[If[n == 1, 1, Function[d, First[Select[Reverse@ First@ d, Times @@ Boole@ Map[# < Last[d]^2 &, FactorInteger[#][[All, 1]]] == 1 &] /. {} -> {1}]]@ {#, First@ Select[#, PrimeQ]} &@ Divisors@ n], {n, 102}] (* _Michael De Vlieger_, Mar 24 2017 *)
%o A284255 (Scheme) (define (A284255 n) (/ n (A284254 n)))
%o A284255 (PARI)
%o A284255 A(n) = if(n<2, return(1), my(f=factor(n)[, 1]); for(i=2, #f, if(f[i]>f[1]^2, return(f[i]))); return(1));
%o A284255 a(n) = if(A(n)==1, 1, A(n)*a(n/A(n)));
%o A284255 for(n=1, 150, print1(n/a(n),", ")) \\ _Indranil Ghosh_, after _David A. Corneth_, Mar 24 2017
%o A284255 (Python)
%o A284255 from sympy import primefactors
%o A284255 def A(n):
%o A284255     pf = primefactors(n)
%o A284255     if pf: min_pf2 = min(pf)**2
%o A284255     for i in pf:
%o A284255         if i > min_pf2: return i
%o A284255     return 1
%o A284255 def a(n): return 1 if A(n)==1 else A(n)*a(n//A(n))
%o A284255 print([n//a(n) for n in range(1, 151)]) # _Indranil Ghosh_, Mar 24 2017
%Y A284255 Cf. A001221, A001222, A006530, A020639, A284252, A284254, A284256, A284257, A284258, A284259, A284260.
%Y A284255 Differs from A284253 for the first time at n=50, where a(50) = 2, while A284253(50) = 10.
%K A284255 nonn
%O A284255 1,2
%A A284255 _Antti Karttunen_, Mar 24 2017