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A046528
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Numbers that are a product of distinct Mersenne primes (elements of A000668).
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11
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1, 3, 7, 21, 31, 93, 127, 217, 381, 651, 889, 2667, 3937, 8191, 11811, 24573, 27559, 57337, 82677, 131071, 172011, 253921, 393213, 524287, 761763, 917497, 1040257, 1572861, 1777447, 2752491, 3120771, 3670009, 4063201, 5332341
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Or, numbers n such that the sum of the divisors of n is a power of 2.
Or, numbers n such that the number of divisors of n and the sum of the divisors of n are both powers of 2.
n is a product of distinct Mersenne primes iff sigma(n) is a power of 2: see exercise in Sivaramakrishnan, or Shallit.
Sequence gives n>1 such that sigma(n)=2*phi(sigma(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 22 2002
Comment from T. D. Noe, Oct 12 2006: The graph of this sequence shows a discontinuity at the 4097th number because there is a large relative gap between the 12th and 13th Mersenne primes, A000043. Other discontinuities can be predicted using A078426.
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REFERENCES
| J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 264 pp. 188, Ellipses Paris 2004.
J. Shallit, Problem 1319, Diophantine Equation, sigma(n) = 2^m, Math. Magazine, 63 (1990), 129.
R. Sivaramakrishnan, Classical Theory of Arithmetic Functions. Dekker, 1989.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..5000
K. S. Brown, Sum of Divisors Equals a Power of 2
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
| a[ 27 ]=1040257=7*127*8191*131071 and Sum[ d ]=1048576 a[ 20 ]=82677=3*7*31*127 and Sum[ d ]=131072
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CROSSREFS
| Cf. A000668, A000043, A046528.
Sequence in context: A003585 A108102 A065523 * A018572 A018641 A097162
Adjacent sequences: A046525 A046526 A046527 * A046529 A046530 A046531
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 22 2002
Further terms from Jon Hart, Sep 22 2006
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Mar 20 2007
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