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A381212 a(n) is the smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of n.

%I A381212 #12 Mar 05 2025 05:36:43
%S A381212 1,1,2,1,1,1,2,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2,1,3,1,1,1,1,2,1,1,1,
%T A381212 2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,
%U A381212 1,1,2,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1
%N A381212 a(n) is the smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of n.
%C A381212 The corresponding largest elements are given by A081812.
%C A381212 The positions of terms > 1 are given by A001694.
%C A381212 Records of a(n) = 2, 3, 4, 5,.. appear at n=4=2^2, 27=3^3, 625=5^4, 3125=5^5, 117649=7^6, 823543=7^7 ,... (subsequence A051647).- _R. J. Mathar_, Mar 05 2025
%H A381212 Paolo Xausa, <a href="/A381212/b381212.txt">Table of n, a(n) for n = 2..10000</a>
%e A381212 a(36) = 2 because 36 = 2^2*3^2, the set of these bases and exponents is {2, 3} and its smallest element is 2.
%e A381212 a(31500) = 1 because 31500 = 2^2*3^2*5^3*7^1, the set of these bases and exponents is {1, 2, 3, 5, 7} and its smallest element is 1.
%p A381212 A381212 := proc(n)
%p A381212     local a,pe;
%p A381212     a := n ;
%p A381212     for pe in ifactors(n)[2] do
%p A381212         a := min(a,op(1,pe),op(2,pe)) ;
%p A381212     end do:
%p A381212     a ;
%p A381212 end proc:
%p A381212 seq(A381212(n),n=2..100) ; # _R. J. Mathar_, Mar 05 2025
%t A381212 A381212[n_] := Min[Flatten[FactorInteger[n]]];
%t A381212 Array[A381212, 100, 2]
%o A381212 (PARI) a(n) = my(f=factor(n)); vecmin(setunion(Set(f[,1]), Set(f[,2]))); \\ _Michel Marcus_, Feb 20 2025
%Y A381212 Cf. A001694, A081812, A288636, A331048, A381201, A381202, A381203, A381204, A381205, A381214.
%K A381212 nonn,easy
%O A381212 2,3
%A A381212 _Paolo Xausa_, Feb 19 2025