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A353694
a(n) is the least multiple of n with mutually distinct exponents in its prime factorization (A130091).
2
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 04 2022
STATUS
approved