On Ruth-Aaron pairs of the second kind
Given a positive integer n with its unique prime factorization given by n = II pi > 1, we define the arithmetic function P by P(n) = p1 + p2 + ... + pr and P(1) = o and w(n) by w(1) = o, w(n) = r. We study pairs (n, n + 1) such that P(n) = P(n + 1) and provide a detailed proof that (5, 6), (24, 2...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
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Animo Repository
2007
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/17467 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | Given a positive integer n with its unique prime factorization given by n = II pi > 1, we define the arithmetic function P by P(n) = p1 + p2 + ... + pr and P(1) = o and w(n) by w(1) = o, w(n) = r. We study pairs (n, n + 1) such that P(n) = P(n + 1) and provide a detailed proof that (5, 6), (24, 25) and (49, 50) are the only pairs (n, n +1) such that {w(n), w(n + 1)} = {1, 2}. Also, we show how to generate certain pairs of the form (2 2n pq, r s) with p < q, r < s odd primes. |
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