A366786 - OEIS

A366786

a(n) = A073481(n)*A005117(n).

1, 4, 9, 25, 12, 49, 20, 121, 169, 28, 45, 289, 361, 63, 44, 529, 52, 841, 60, 961, 99, 68, 175, 1369, 76, 117, 1681, 84, 1849, 92, 2209, 153, 2809, 275, 171, 116, 3481, 3721, 124, 325, 132, 4489, 207, 140, 5041, 5329, 148, 539, 156, 6241, 164, 6889, 425, 172

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OFFSET

1,2

COMMENTS

Define f(x) to be lpf(k)*k, where lpf(k) = A020639(k). This sequence contains the mappings of f(x) across squarefree numbers A005117.

a(1) = 1 by definition. 1 is the empty product and has no least prime factor.

Define sequence R_k = { m : rad(m) | k }, where rad(n) = A007947(n) and k > 1 is squarefree. Then the sequence k*R_k contains all numbers divisible by squarefree k that are also not divisible by any prime q coprime to k.

Plainly, k is the first term in the sequence k*R_k, because 1 is the first term in R_k. Hence a(n) is the second term in k*R_k for n > 1, since lpf(k) is the second term in R_k.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A065642(A005117(n)), n > 1.

a(n) = A285109(A005117(n)).

a(n) = A020639(A005117(n))*A005117(n).

For prime p, a(p) = p^2.

For composite squarefree k, a(k) = (p^2 * m) such that (p^2 * m) is in A364996.

Permutation of the union of {1}, A001248, and A366825.

EXAMPLE

Let b(n) = A005117(n).

a(2) = 4 = b(2)*lpf(b(2)) = 2*lpf(2) = 2*2. In {2*A000079}, 4 is the second term.