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A284260 Greatest prime dividing n which is less than A020639(n)^2, where A020639(n) is the smallest prime dividing n, a(1) = 1.

%I A284260 #18 Apr 29 2021 12:33:07
%S A284260 1,2,3,2,5,3,7,2,3,2,11,3,13,2,5,2,17,3,19,2,7,2,23,3,5,2,3,2,29,3,31,
%T A284260 2,3,2,7,3,37,2,3,2,41,3,43,2,5,2,47,3,7,2,3,2,53,3,11,2,3,2,59,3,61,
%U A284260 2,7,2,13,3,67,2,3,2,71,3,73,2,5,2,11,3,79,2,3,2,83,3,17,2,3,2,89,3,13,2,3,2,19,3,97,2,3,2,101,3,103,2,7,2,107,3,109
%N A284260 Greatest prime dividing n which is less than A020639(n)^2, where A020639(n) is the smallest prime dividing n, a(1) = 1.
%H A284260 Antti Karttunen, <a href="/A284260/b284260.txt">Table of n, a(n) for n = 1..10001</a>
%F A284260 a(n) = A006530(A284255(n)).
%t A284260 Table[Last[Function[s, Select[s, # < First[s]^2 &]]@ FactorInteger[n][[All, 1]] /. {} -> {1}], {n, 109}] (* _Michael De Vlieger_, Mar 24 2017 *)
%o A284260 (Scheme) (define (A284260 n) (A006530 (A284255 n)))
%o A284260 (PARI) 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 A284260 a(n) = if(A(n)==1, 1, A(n)*a(n/A(n)));
%o A284260 gpf(n) = if(n>1, vecmax(factor(n)[,1]),1);
%o A284260 for(n=1, 150, print1(gpf(n/a(n)),", ")) \\ _Indranil Ghosh_, Mar 24 2017, after _David A. Corneth_
%o A284260 (Python)
%o A284260 from sympy import primefactors
%o A284260 def A(n):
%o A284260     for i in primefactors(n):
%o A284260         if i>min(primefactors(n))**2: return i
%o A284260     return 1
%o A284260 def a(n): return 1 if A(n)==1 else A(n)*a(n//A(n))
%o A284260 def gpf(n): return 1 if n<2 else max(primefactors(n))
%o A284260 print([gpf(n//a(n)) for n in range(1, 151)]) # _Indranil Ghosh_, Mar 24 2017
%Y A284260 Cf. A006530, A020639, A284252, A284253, A284254, A284255, A284256, A284257, A284258, A284259.
%Y A284260 Cf. A251726 (gives n > 1 such that a(n) = A006530(n)).
%K A284260 nonn
%O A284260 1,2
%A A284260 _Antti Karttunen_, Mar 24 2017