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

%I A290107 #15 Aug 15 2017 20:34:21
%S A290107 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,
%T A290107 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,
%U A290107 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
%N A290107 a(1) = 1; for n > 1, a(n) = product of distinct exponents in the prime factorization of n.
%H A290107 Antti Karttunen, <a href="/A290107/b290107.txt">Table of n, a(n) for n = 1..10000</a>
%H A290107 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A290107 a(n) = A156061(A181819(n)).
%e A290107 For n = 36 = 2^2 * 3^2, the only distinct exponent that occurs is 2, thus a(36) = 2.
%e A290107 For n = 144 = 2^4 * 3^2, the distinct exponents are 2 and 4, thus a(144) = 2*4 = 8.
%e A290107 For n = 4500 = 2^2 * 3^2 * 5^3, the distinct exponents are 2 and 3, thus a(4500) = 2*3 = 6.
%t A290107 Table[If[n == 1, 1, Apply[Times, Union[FactorInteger[n][[All, -1]] ]]], {n, 120}] (* _Michael De Vlieger_, Aug 14 2017 *)
%o A290107 (PARI) A290107(n) = factorback(vecsort((factor(n)[, 2]), ,8));
%o A290107 (Scheme) (define (A290107 n) (A156061 (A181819 n)))
%Y A290107 Cf. A156061, A181819.
%Y A290107 Differs from A005361 for the first time at n=36.
%Y A290107 Differs from A072411 for the first time at n=144, and also from A157754 for the second time (after the initial term).
%K A290107 nonn
%O A290107 1,4
%A A290107 _Antti Karttunen_, Aug 13 2017