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A290107
a(1) = 1; for n > 1, a(n) = product of distinct exponents in the prime factorization of n.
7
1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 5, 1, 2, 2, 2, 1, 1, 1, 3, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 3
OFFSET
1,4
FORMULA
a(n) = A156061(A181819(n)).
EXAMPLE
For n = 36 = 2^2 * 3^2, the only distinct exponent that occurs is 2, thus a(36) = 2.
For n = 144 = 2^4 * 3^2, the distinct exponents are 2 and 4, thus a(144) = 2*4 = 8.
For n = 4500 = 2^2 * 3^2 * 5^3, the distinct exponents are 2 and 3, thus a(4500) = 2*3 = 6.
MATHEMATICA
Table[If[n == 1, 1, Apply[Times, Union[FactorInteger[n][[All, -1]] ]]], {n, 120}] (* Michael De Vlieger, Aug 14 2017 *)
PROG
(PARI) A290107(n) = factorback(vecsort((factor(n)[, 2]), , 8));
(Scheme) (define (A290107 n) (A156061 (A181819 n)))
CROSSREFS
Differs from A005361 for the first time at n=36.
Differs from A072411 for the first time at n=144, and also from A157754 for the second time (after the initial term).
Sequence in context: A324912 A157754 A072411 * A375136 A212180 A091050
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 13 2017
STATUS
approved