A353694 a(n) is the least multiple of n with mutually distinct exponents in its prime factorization (A130091).

1, 2, 3, 4, 5, 12, 7, 8, 9, 20, 11, 12, 13, 28, 45, 16, 17, 18, 19, 20, 63, 44, 23, 24, 25, 52, 27, 28, 29, 360, 31, 32, 99, 68, 175, 72, 37, 76, 117, 40, 41, 504, 43, 44, 45, 92, 47, 48, 49, 50, 153, 52, 53, 54, 275, 56, 171, 116, 59, 360, 61, 124, 63, 64, 325

Offset: 1

Author

Amiram Eldar, May 04 2022

Keywords

• nonn

Examples

			a(2) = 2 since 2 = 2^1 has only one exponent (1) in its prime factorization.
a(6) = 12 since 6 = 2*3 has two equal exponents (1) in its prime factorization, and 2*6 = 12 = 2^2*3 has two distinct exponents (1 and 2).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A130091, A130092, A353693.

Programs

Mathematica

a[n_] := Module[{k = n}, While[!UnsameQ @@ FactorInteger[k][[;; , 2]], k += n]; k]; Array[a, 100]

Formula

a(n) = n if and only if n is in A130091.

a(A130092(n)) > n.

a(n) = n * A353693(n).