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Search: id:A130075
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| A130075 |
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Quotients (5^p - 3^p - 2^p)/p, where p = Prime(n). |
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5
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| 6, 30, 570, 10830, 4422630, 93776970, 44871187170, 1003806502230, 518297165370030, 6422911941109705770, 150213298561349961630, 1966475018690546370358170, 1109139879321302763891656370
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OFFSET
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1,1
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COMMENT
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p divides 5^p - 3^p - 2^p = A130072(p) for prime p. p^(k+1) divides A130072(p^k) for prime p = {2,3,5,19} = A130076(n) and all k>0. 2 divides a(n). 3 divides a(n). 5 divides a(n) for n>1. 19 divides a(n) for n>2. 19^2 divides a(n) for n = {4,6,8,11,12,14,...} = A091178(n) n-th prime is of the form 6n+1; or Prime(n) = {7,13,19,31,37,43,...} = A002476 Primes of form 6n + 1.
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FORMULA
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a(n) = (5^Prime[n] - 3^Prime[n] - 2^Prime[n])/Prime[n]. a(n) = A130072(Prime(n))/Prime(n).
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MATHEMATICA
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Table[(5^Prime[n]-3^Prime[n]-2^Prime[n])/Prime[n], {n, 1, 20}]
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CROSSREFS
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Cf. A130072, A130073, A130074, A130076, A091178, A002476.
Sequence in context: A111876 A119634 A075591 this_sequence A066388 A088256 A136349
Adjacent sequences: A130072 A130073 A130074 this_sequence A130076 A130077 A130078
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), May 06 2007
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