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Search: id:A080086
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| A080086 |
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Number of factors of 3 in the factorial of the n-th prime, counted with multiplicity. |
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+0
5
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| 0, 1, 1, 2, 4, 5, 6, 8, 9, 13, 14, 17, 18, 19, 21, 23, 27, 28, 31, 32, 34, 36, 40, 42, 46, 48, 49, 50, 53, 54, 61, 62, 66, 67, 71, 72, 75, 80, 81, 84, 86, 88, 93, 94, 95, 97, 102, 108, 110, 111, 112, 115, 116, 123, 126, 129, 131, 134, 136, 138, 139, 143, 151, 152, 153
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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a(n) = sum_{k=1..L} floor( p_n /3^k ), where L = ln(p_n)/ln(3), where p_n is the n-th prime.
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MATHEMATICA
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lst={}; Do[p=Prime[n]; s=0; While[p>1, p=IntegerPart[p/3]; s+=p; ]; AppendTo[lst, s], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 28 2009]
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CROSSREFS
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Cf. A080084, A080085, A080087.
Sequence in context: A161793 A048262 A030326 this_sequence A015844 A114318 A035500
Adjacent sequences: A080083 A080084 A080085 this_sequence A080087 A080088 A080089
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 26 2003
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