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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2007
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oai:animorepository.dlsu.edu.ph:etd_bachelors-179802022-02-04T05:10:12Z On Ruth-Aaron pairs of the second kind Mordeno, Mark Oyelle Yacapin, John Mark 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. 2007-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/17467 Bachelor's Theses English Animo Repository Arithmetic functions Number theory |
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Philippines Philippines |
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English |
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Arithmetic functions Number theory |
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Arithmetic functions Number theory Mordeno, Mark Oyelle Yacapin, John Mark On Ruth-Aaron pairs of the second kind |
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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. |
| format |
text |
| author |
Mordeno, Mark Oyelle Yacapin, John Mark |
| author_facet |
Mordeno, Mark Oyelle Yacapin, John Mark |
| author_sort |
Mordeno, Mark Oyelle |
| title |
On Ruth-Aaron pairs of the second kind |
| title_short |
On Ruth-Aaron pairs of the second kind |
| title_full |
On Ruth-Aaron pairs of the second kind |
| title_fullStr |
On Ruth-Aaron pairs of the second kind |
| title_full_unstemmed |
On Ruth-Aaron pairs of the second kind |
| title_sort |
on ruth-aaron pairs of the second kind |
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Animo Repository |
| publishDate |
2007 |
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https://animorepository.dlsu.edu.ph/etd_bachelors/17467 |
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1772835203799056384 |