

A290107


a(1) = 1; for n > 1, a(n) = product of distinct exponents in the prime factorization of n.


5



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
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OFFSET

1,4


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from exponents in factorization of n


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

Cf. A156061, A181819.
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 * A212180 A091050 A005361
Adjacent sequences: A290104 A290105 A290106 * A290108 A290109 A290110


KEYWORD

nonn


AUTHOR

Antti Karttunen, Aug 13 2017


STATUS

approved



