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Search: id:A109325
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| A109325 |
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Zsigmondy numbers for a = 3, b = 2: Zs(n, 3, 2) is the greatest divisor of 3^n - 2^n (A001047) that is relatively prime to 3^m - 2^m for all positive integers m < n. |
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+0
6
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| 1, 5, 19, 13, 211, 7, 2059, 97, 1009, 11, 175099, 61, 1586131, 463, 3571, 6817, 129009091, 577, 1161737179, 4621, 267331, 35839, 94134790219, 5521, 4015426801, 320503, 397760329, 369181, 68629840493971, 7471, 617671248800299, 43112257
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The full factorization is multiplicative; meaning that the composition of factors is determined by the prime-factorization of n.
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LINKS
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Eric Weisstein's World of Mathematics, Zsigmondy's Theorem
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EXAMPLE
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Let n be 7; then the factorization of g(n) := 3^n-2^n is then g(7) = A(7) = 2059 since n is prime; let n be 3 then the factorization of g(3) = A(3) = 19 since n is prime; let n be 21, then the factorization is g(21) = A(3)*A(7)*A(21); and whether n is composite or not, with each n (at least) one new factor occurs besides the factors determined by the prime factors of n - so it is not purely multiplicative.
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CROSSREFS
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Cf. A064078-A064083, A109347, A109348, A109349.
Sequence in context: A089082 A106229 A129734 this_sequence A166639 A032731 A087840
Adjacent sequences: A109322 A109323 A109324 this_sequence A109326 A109327 A109328
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KEYWORD
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nonn
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AUTHOR
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Gottfried Helms (helms(AT)uni-kassel.de), Aug 09 2005
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EXTENSIONS
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Edited and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Aug 26 2005
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