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

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, 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, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 2

Author

Paolo Xausa, Feb 19 2025

Keywords

• nonn
• easy

Comments

The corresponding largest elements are given by A081812.

The positions of terms > 1 are given by A001694.

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

Examples

			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.
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.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A001694, A081812, A288636, A331048, A381201, A381202, A381203, A381204, A381205, A381214.

Programs

Maple

A381212 := proc(n)
    local a,pe;
    a := n ;
    for pe in ifactors(n)[2] do
        a := min(a,op(1,pe),op(2,pe)) ;
    end do:
    a ;
end proc:
seq(A381212(n),n=2..100) ; # R. J. Mathar, Mar 05 2025

Mathematica

A381212[n_] := Min[Flatten[FactorInteger[n]]];
Array[A381212, 100, 2]

PARI

a(n) = my(f=factor(n)); vecmin(setunion(Set(f[,1]), Set(f[,2]))); \\ Michel Marcus, Feb 20 2025