A290107 a(1) = 1; for n > 1, a(n) = product of distinct exponents in the prime factorization of n.

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

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