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%I #33 May 07 2021 10:42:41
%S 1,1,1,1,1,1,1,1,1,5,1,1,1,7,1,1,1,1,1,5,1,11,1,1,1,13,1,7,1,5,1,1,11,
%T 17,1,1,1,19,13,5,1,7,1,11,1,23,1,1,1,25,17,13,1,1,1,7,19,29,1,5,1,31,
%U 1,1,1,11,1,17,23,35,1,1,1,37,1,19,1,13,1,5,1,41,1,7,1,43,29,11,1,5,1,23,31,47,1,1,1,49,11,25,1,17,1,13,1,53,1,1,1,55
%N Largest divisor of n such that all its prime factors are greater than the square of smallest prime factor of n, a(1) = 1.
%H Antti Karttunen, <a href="/A284254/b284254.txt">Table of n, a(n) for n = 1..10001</a>
%F If A284252(n) = 1, then a(n) = 1, otherwise A284252(n) * a(A284253(n)).
%F Other identities. For all n >= 1:
%F n / a(n) = A284255(n).
%F A020639(a(n)) = A284252(n).
%F A001221(a(n)) = A284258(n).
%F A001222(a(n)) = A284256(n).
%e For n = 15 = 3*5, no prime factor is larger than 3^2, thus a(15) = 1. In this case the largest divisor satisfying the condition has no prime factors at all.
%e For n = 50 = 2*5*5, the primes larger than 2^2 are 5 and 5, thus a(50) = 5*5 = 25.
%t Table[If[n == 1, 1, Function[d, Last[Select[Reverse@ First@ d, Times @@ Boole@ Map[# > Last[d]^2 &, FactorInteger[#][[All, 1]]] == 1 &] /. {} -> {1}]]@ {#, First@ Select[#, PrimeQ]} &@ Divisors@ n], {n, 108}] (* _Michael De Vlieger_, Mar 24 2017 *)
%o (Scheme, with memoization-macro definec)
%o (definec (A284254 n) (if (= 1 (A284252 n)) 1 (* (A284252 n) (A284254 (A284253 n)))))
%o (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 a(n) = if(A(n)==1, 1, A(n)*a(n/A(n)));
%o for(n=1, 150, print1(a(n),", ")) \\ _Indranil Ghosh_, after _David A. Corneth_, Mar 24 2017
%o (Python)
%o from sympy import primefactors
%o def A(n):
%o for i in primefactors(n):
%o if i>min(primefactors(n))**2: return i
%o return 1
%o def a(n): return 1 if A(n) == 1 else A(n)*a(n//A(n))
%o print([a(n) for n in range(1, 151)]) # _Indranil Ghosh_, Mar 24 2017
%Y Cf. A020639, A284253, A284255, A284256, A284257, A284258, A284259, A284260.
%Y Cf. A251726 (gives the positions of ones after the initial a(1)=1).
%Y Differs from related A284252 for the first time at n=50, where a(50) = 25, while A284252(50) = 5.
%K nonn
%O 1,10
%A _Antti Karttunen_, Mar 24 2017
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