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Search: id:A073087
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| A073087 |
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Least k such that sigma(k^k)>=n*k^k. |
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+0
1
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| 1, 6, 30, 210, 30030, 223092870, 13082761331670030, 3217644767340672907899084554130, 1492182350939279320058875736615841068547583863326864530410
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Does a(n) = the product of primes less than or equal to prime(n+1) = A002110(n+1)? Answer from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Sep 14 2005: No, this is not true.
Comment from Mitch Harris, Sep 14 2005: Note that sigma(k^k) = prod (p^(k r + 1) - 1)/(p - 1).
Comment from David W. Wilson (davidwwilson(AT)comcast.net), Sep 14 2005: I have proved to my own satisfaction that for n >= 4, A073087(n) = p#, where p is the smallest prime satisfying p#/phi(p#) >= n. See link.
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LINKS
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David W. Wilson, Comments on this sequence
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FORMULA
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a(n) = A091440(n)# = A002110(A112873(n)) for n >= 4.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, s=1; while(sigma(s^s)<n*s^s, s++); s)
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CROSSREFS
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Cf. A023199.
Sequence in context: A057896 A054721 A074111 this_sequence A126751 A009689 A133668
Adjacent sequences: A073084 A073085 A073086 this_sequence A073088 A073089 A073090
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 18 2002
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net), Sep 15 2005
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