cp's OEIS Frontend

A284252 a(n) = smallest prime dividing n which is larger than the square of smallest prime dividing n, or 1 if no such prime exists, a(1) = 1.

%I A284252 #27 Mar 27 2021 06:17:53
%S A284252 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 A284252 17,1,1,1,19,13,5,1,7,1,11,1,23,1,1,1,5,17,13,1,1,1,7,19,29,1,5,1,31,
%U A284252 1,1,1,11,1,17,23,5,1,1,1,37,1,19,1,13,1,5,1,41,1,7,1,43,29,11,1,5,1,23,31,47,1,1,1,7,11,5,1,17,1,13,1,53,1,1,1,5,37
%N A284252 a(n) = smallest prime dividing n which is larger than the square of smallest prime dividing n, or 1 if no such prime exists, a(1) = 1.
%H A284252 Antti Karttunen, <a href="/A284252/b284252.txt">Table of n, a(n) for n = 1..10001</a>
%F A284252 a(n) = A020639(A284254(n)).
%F A284252 a(k) > 1 iff k is in A251727. - _David A. Corneth_, Mar 25 2017
%e A284252 For n=10 = 2*5, the smallest prime divisor > 2^2 is 5, thus a(10) = 5.
%e A284252 For n=15 = 3*5, there are no prime divisors > 3^2, thus a(15) = 1.
%e A284252 For n=165 = 3*5*11, the smallest prime divisor > 3^2 is 11, thus a(165) = 11.
%t A284252 a[n_] := Block[{p = First /@ FactorInteger[n]}, SelectFirst[p, # > p[[1]]^2 &, 1]]; Array[a, 120] (* _Giovanni Resta_, Mar 24 2017 *)
%o A284252 (Scheme) (define (A284252 n) (let ((spf1 (A020639 n))) (let loop ((n (/ n spf1))) (let ((spf2 (A020639 n))) (cond ((= 1 spf2) 1) ((> spf2 (* spf1 spf1)) spf2) (else (loop (/ n spf2))))))))
%o A284252 (PARI) a(n) = if(n==1, return(1), my(f=factor(n)[, 1]); s = f[1]; for(i=2,#f, if(f[i]>s^2, return(f[i]))); return(1)) \\ _David A. Corneth_, Mar 24 2017
%o A284252 (Python)
%o A284252 from sympy import primefactors
%o A284252 def a(n):
%o A284252     for i in primefactors(n):
%o A284252         if i>min(primefactors(n))**2: return i
%o A284252     return 1
%o A284252 print([a(n) for n in range(1, 151)]) # _Indranil Ghosh_, Mar 24 2017
%Y A284252 Cf. A020639, A284253, A284254, A284255, A284256, A284257, A284258, A284259, A284260.
%Y A284252 Cf. A251726 (gives the positions of ones after the initial a(1) = 1), A251727 (positions of terms > 1).
%K A284252 nonn
%O A284252 1,10
%A A284252 _Antti Karttunen_, Mar 24 2017