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 A165715 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 {p(n,k)^b(A165713(n), k)}. 1
 2, 9, 2, 5, 6, 343, 4, 3, 20, 11, 6, 28561, 14, 75, 2, 17, 12, 19, 10, 21, 88, 529, 6, 125, 52, 3, 14, 29, 30, 28629151, 2, 33, 34, 1225, 6, 37, 38, 351, 20, 41, 84, 43, 44, 15, 368, 2209, 18, 7, 10, 153, 4394, 53, 6, 1375, 14, 57, 58, 59, 30, 51520374361, 124, 21, 2 (list; graph; refs; listen; history; text; internal format)
 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..64. 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 12 and the exponents from the factorization of 14, we have a(12) = 2^1 * 3^1 = 6. CROSSREFS Cf. A165713, A165714. Sequence in context: A188981 A277754 A112537 * A088928 A074957 A196401 Adjacent sequences: A165712 A165713 A165714 * A165716 A165717 A165718 KEYWORD nonn AUTHOR Leroy Quet, Sep 24 2009 EXTENSIONS Extended by Ray Chandler, Mar 12 2010 STATUS approved

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Last modified September 22 11:51 EDT 2023. Contains 365531 sequences. (Running on oeis4.)