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Search: id:A083346
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| A083346 |
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Denominator of r(n) = Sum(e/p: n=Prod(p^e)). |
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4
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| 1, 2, 3, 1, 5, 6, 7, 2, 3, 10, 11, 3, 13, 14, 15, 1, 17, 6, 19, 5, 21, 22, 23, 6, 5, 26, 1, 7, 29, 30, 31, 2, 33, 34, 35, 3, 37, 38, 39, 10, 41, 42, 43, 11, 15, 46, 47, 3, 7, 10, 51, 13, 53, 2, 55, 14, 57, 58, 59, 15, 61, 62, 21, 1, 65, 66, 67, 17, 69, 70, 71, 6, 73, 74, 15, 19, 77, 78
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OFFSET
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1,2
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COMMENT
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Multiplicative with a(p^e) = 1 iff p|e, p otherwise. For f(n) = A083345(n)/A083346(n), f(p^i*q^j*...) = f(p^i)+f(q^j)+... The denominator of each term is 1 or the prime, thus the denominator of the sum is the product of the denominators of the components. Christian G. Bower (bowerc(AT)usa.net) May 16, 2005.
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EXAMPLE
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n=12 = 2*2*3 = 2^2 * 3^1 -> r(12) = 2/2 + 1/3 = (6+2)/6, therefore a(12)=3, A083345(12)=4;
n=18 = 2*3*3 = 2^1 * 3^2 -> r(18) = 1/2 + 2/3 = (3+4)/6, therefore a(18)=6, A083345(18)=7.
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CROSSREFS
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Numerator: A083345, A072873, A083347, A083348.
Adjacent sequences: A083343 A083344 A083345 this_sequence A083347 A083348 A083349
Sequence in context: A055231 A072400 A007913 this_sequence A065883 A071975 A055905
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KEYWORD
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nonn,mult
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Apr 25 2003
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