cp's OEIS Frontend

A134194 a(n) = the smallest positive divisor of n that does not occur among the exponents in the prime factorization of n.

%I A134194 #17 May 09 2021 05:06:32
%S A134194 1,2,3,1,5,2,7,1,1,2,11,3,13,2,3,1,17,3,19,4,3,2,23,2,1,2,1,4,29,2,31,
%T A134194 1,3,2,5,1,37,2,3,2,41,2,43,4,3,2,47,2,1,5,3,4,53,2,5,2,3,2,59,3,61,2,
%U A134194 3,1,5,2,67,4,3,2,71,1,73,2,3,4,7,2,79,2,1,2,83,3,5,2,3,2,89,3,7,4,3,2,5,2
%N A134194 a(n) = the smallest positive divisor of n that does not occur among the exponents in the prime factorization of n.
%C A134194 If n is in A008578, a(n) = n. - _Indranil Ghosh_, May 16 2017
%H A134194 Indranil Ghosh, <a href="/A134194/b134194.txt">Table of n, a(n) for n = 1..10000</a>
%e A134194 The prime factorization of 24 is 2^3 * 3^1. The exponents are 3 and 1. The positive divisors of 24 are 1,2,3,4,6,8,12,24. Therefore since only the divisors 1 and 3 occur among the exponents in the prime factorization of 24, then a(24) = 2 is the smallest divisor not occurring among those exponents.
%e A134194 The prime factorization of 40 is 2^3 * 5^1. The exponents are 3 and 1. The positive divisors of 40 are 1,2,4,5,8,10,20,40. Therefore since only the divisor 1 occurs among the exponents in the prime factorization of 40, then a(40) = 2 is the smallest divisor not occurring among those exponents.
%t A134194 Table[Min[Complement[Divisors[n], Table[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}]]], {n, 1, 80}] (* _Stefan Steinerberger_, Aug 30 2008 *)
%o A134194 (Python)
%o A134194 from sympy import divisors, factorint
%o A134194 def a(n):
%o A134194     f=factorint(n)
%o A134194     l=[f[i] for i in f]
%o A134194     return min(i for i in divisors(n) if i not in l)
%o A134194 print([a(n) for n in range(1, 97)]) # _Indranil Ghosh_, May 16 2017
%K A134194 nonn
%O A134194 1,2
%A A134194 _Leroy Quet_, Jan 13 2008
%E A134194 Corrected and extended by _Stefan Steinerberger_, Aug 30 2008