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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 3 19:43 EDT 2020. Contains 333198 sequences. (Running on oeis4.)