A165714 - OEIS

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A165714

Let the prime factorization of m be m = product p(m,k)^b(m,k), where p(m,j)<p(m,j+1) for all j, the p's are the distinct primes dividing m, and each b is a positive integer. Then a(n) = product_k {p(A165713(n), k)^b(n,k)}.

3, 2, 25, 7, 10, 2, 27, 121, 6, 13, 28, 2, 15, 6, 83521, 19, 50, 23, 63, 22, 6, 5, 104, 9, 14, 24389, 99, 31, 42, 2, 69343957, 34, 35, 6, 1444, 41, 39, 10, 88, 43, 30, 47, 45, 92, 6, 7, 80, 2809, 867, 26, 12, 59, 6655, 14, 513, 58, 62, 61, 132, 2, 21, 325, 90458382169, 34

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OFFSET

2,1

COMMENTS

A165713(n) = the smallest integer > n that is divisible by exactly the same number of distinct primes as n is.

LINKS

Table of n, a(n) for n=2..65.

EXAMPLE

12 = 2^2 * 3^1, which is divisible by 2 distinct primes. The next larger integer divisible by exactly 2 distinct primes is 14 = 2^1 * 7^1. Taking the primes from the factorization of 14 and the exponents from the factorization of 12, we have a(12) = 2^2 * 7^1 = 28.

CROSSREFS

Cf. A165713, A165715.

Sequence in context: A151475 A105525 A228772 * A090883 A100645 A132960

Adjacent sequences: A165711 A165712 A165713 * A165715 A165716 A165717

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 24 2009

EXTENSIONS

Extended by Ray Chandler, Mar 12 2010

STATUS

approved