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Search: id:A072942
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| A072942 |
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Smallest number x such that x^n-1 factors only into its algebraic factors. |
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+0
1
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| 3, 4, 3, 4, 12, 6, 3, 4, 3, 12, 20, 24687390, 3, 72, 62, 4, 20, 107354724540, 12, 58051620, 3, 1793172, 468, 1035844571580, 62, 882, 398
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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An exactly equivalent formulation is that a(n) is the least x such that the cyclotomic polynomial values Phi(d,x) are prime for all d dividing n. Many more terms are known, in particular terms at prime indices. Massively composite n are the hardest to find - term 256 alone took a month to find. Contact the author for more terms beyond the gaps.
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EXAMPLE
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a(16)=4 because 4^16-1 = 3.5.17.257.65537, which are the 5 algebraic factors.
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PROGRAM
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(PARI) for(d=1, 17, ds=divisors(d); print("Searching for d|"d":"ds); forprime(p=2, 499999, okc=1; for(c=2, length(ds), if(!isprime(subst(polcyclo(ds[c]), x, p+1)), okc=0; break)); if(okc, for(c=1, length(ds), print("Phi("ds[c]", "p+1")="subst(polcyclo(ds[c]), x, p+1))); break)))
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CROSSREFS
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Cf. A070737.
Sequence in context: A135800 A006984 A087275 this_sequence A025267 A090739 A076400
Adjacent sequences: A072939 A072940 A072941 this_sequence A072943 A072944 A072945
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KEYWORD
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nonn
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AUTHOR
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Phil Carmody (pc+oeis(AT)asdf.org), Aug 12 2002
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