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Search: id:A089631
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| A089631 |
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a(n) = (Product_{p is a prime factor of n} p)) mod (Product_{p is a prime factor of n} p-1). |
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+0
1
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| 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 7, 0, 1, 0, 1, 2, 9, 2, 1, 0, 1, 2, 1, 2, 1, 6, 1, 0, 13, 2, 11, 0, 1, 2, 15, 2, 1, 6, 1, 2, 7, 2, 1, 0, 1, 2, 19, 2, 1, 0, 15, 2, 21, 2, 1, 6, 1, 2, 9, 0, 17, 6, 1, 2, 25, 22, 1, 0, 1, 2, 7, 2, 17, 6, 1, 2, 1, 2, 1, 6, 21, 2, 31, 2, 1, 6, 19, 2, 33, 2, 23, 0, 1, 2, 13
(list; graph; listen)
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OFFSET
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2,9
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COMMENT
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It can be shown that the unsolved problem of finding a composite solution n of the congruence n-1 = 1 mod phi(n) is equivalent to finding a square-free composite number n such a(n) = 1.
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LINKS
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C. Rivera, Puzzle 248, The Prime Puzzles and Problems Connection
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EXAMPLE
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Let n = 10; then Product_{p is a prime factor of 10} p = 2 x 5 = 10, Product_{p is a prime factor of 10} p-1 = (2-1) x (5-1) = 10.
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MATHEMATICA
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p[n_] := Transpose[FactorInteger[n]][[1]]; t = Table[p[i], {i, 2, 100}]; r = {}; s = {}; For[i = 1, i <= 99, i++, r = Append[r, Product[t[[i]][[j]], {j, 1, Length[t[[i]]]}]]; s = Append[s, Product[t[[i]][[j]] - 1, {j, 1, Length[t[[i]]]}]]]; Mod[r, s]
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CROSSREFS
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Sequence in context: A129620 A074766 A138107 this_sequence A129558 A131185 A052249
Adjacent sequences: A089628 A089629 A089630 this_sequence A089632 A089633 A089634
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 04 2004
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