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Search: id:A086252
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| A086252 |
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a(n) is the smallest k such that 2^k-1 has n primitive prime factors. |
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+0
3
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OFFSET
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1,1
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COMMENT
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A prime factor of 2^n-1 is called primitive if it does not divide 2^r-1 for any r<n. Equivalently, p is a primitive prime factor of 2^n-1 if ord(2,p)=n. See A086251 for the number of primitive prime factors in 2^n-1.
No more terms < 673. (2^673-1 is the first that isn't completely factored in the linked reference.) - David Wasserman (wasserma(AT)spawar.navy.mil), Feb 22 2005
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REFERENCES
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J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
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LINKS
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J. Brillhart et al., Factorizations of b^n +- 1 Available on-line
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EXAMPLE
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a(2) = 11 because 2^11-1 = 23*89, both 23 and 89 have order 11, and the numbers 2^r-1 have only 0 or 1 primitive prime factors.
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CROSSREFS
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Cf. A086251.
Sequence in context: A024178 A009312 A092275 this_sequence A106926 A133558 A062802
Adjacent sequences: A086249 A086250 A086251 this_sequence A086253 A086254 A086255
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KEYWORD
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hard,more,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jul 14 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Feb 22 2005
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