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 A074777 Integers n such that sigma(phi(n))/n = 1/2. 1
 2, 6, 30, 510, 131070, 8589934590 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Since 2^(2^n)+1 is prime for n=0,1,...,4 (Fermat primes), 2^(2^(n-1)+1)-2 is in the sequence for n=1,2,...,6. Conjecture: There are no further terms. - Farideh Firoozbakht, Sep 14 2004 For k of the form 2^m and in the interval [a(n)/a(n-1) - 2, a(n+1)/a(n) - 2], with a(0) = 1, the numbers x such that u^k + (u+1)^k + ... + (u+x-1)^k is prime for some u are the divisors of a(n) (excluding 1 as a divisor for n > 1). Example: n = 4. The interval [a(4)/a(3) - 2, a(5)/a(4) - 2] = [15, 255]. The numbers of the form 2^m for some m in this interval are 16 = 2^4, 32 = 2^5, 64 = 2^6, and 128 = 2^7. Taking k = 16 (for example), numbers x such that u^16 + (u+1)^16 + ... + (u+x-1)^16 is prime for some u are {2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510} which are the divisors of a(4). This is also true when the exponent is 32, 64, or 128. - Derek Orr, Jun 13 2014 LINKS Table of n, a(n) for n=1..6. FORMULA For n=1, 2, ..., 6, a(n)=2^(2^(n-1)+1)-2. - Farideh Firoozbakht, Sep 14 2004 CROSSREFS Cf. A062402, A019434. Sequence in context: A112723 A326867 A320830 * A007280 A280260 A102927 Adjacent sequences: A074774 A074775 A074776 * A074778 A074779 A074780 KEYWORD nonn AUTHOR Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002 EXTENSIONS 8589934590 from Farideh Firoozbakht, Sep 14 2004 STATUS approved

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Last modified August 11 05:00 EDT 2024. Contains 375059 sequences. (Running on oeis4.)