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%I #14 Jun 20 2019 17:51:30
%S 1,2,3,4,5,4,6,6,7,8,9,8,10,12,9,12,15,8,10,14,16,18,12,11,16,20,21,
%T 16,12,18,24,18,24,20,25,13,20,28,24,27,24,30,14,22,32,30,27,30,28,35,
%U 32,15,24,36,36,16,36,36,33,32,40,40,16,26,40,42,24,42,45
%N a(n) = product of exponents in canonical prime factorization of A181800(n) (n-th powerful number that is the first integer of its prime signature); a(1) = 1 by convention.
%C The product of exponents in the canonical prime factorization of n, or A005361(n), is a function of the second signature of n (cf. A212172). Since A181800 consists of the first integer of each second signature, this sequence gives the value of A005361 for each second signature in order of its first appearance.
%C a(n) also gives the number of divisors of A212638(n), a permutation of A025487. Each positive integer n appears A001055(n) times in this sequence.
%H Amiram Eldar, <a href="/A212647/b212647.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A005361(A181800(n)).
%F a(n) = A000005(A212638(n)).
%e The product of the exponents in the prime factorization of 144 (2^4*3^2) is 4*2 = 8. Since 144 = A181800(10), a(10) = 8.
%Y Cf. A005361, A181800, A212172, A212638.
%K nonn
%O 1,2
%A _Matthew Vandermast_, Jun 09 2012
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