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

1,2

Links

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

Formula

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

a(A130092(n)) > n.

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

Example

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).

Mathematica

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

Crossrefs

Cf. A130091, A130092, A353693.

Sequence in context: A330263 A369864 A065636 * A328260 A229347 A367167

Adjacent sequences: A353691 A353692 A353693 * A353695 A353696 A353697

Keyword

nonn

Author

Amiram Eldar, May 04 2022

Status

approved