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Search: id:A006881
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| A006881 |
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Numbers that are the product of two distinct primes.
(Formerly M4082)
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+0
105
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| 6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Numbers n such that phi(n)+sigma(n)=2*(n+1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 02 2002
n such that tau(n)=omega(n)^omega(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 10 2002
Could also be called square-free semiprimes (or 2-almost primes). - Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 11 2003
Goldston et al. proved that lim inf [as n approaches infinity] (a(n+1) - a(n)) =< 26. If an appropriate generalization of the Elliott-Halberstam Conjecture is true, then the above bound can be improved to 6. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 20 2005
A000005(a(n)^(k-1)) = A000290(k) for all k>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2007
The maximal number of consecutive integers in this sequence is 3 - there can not be 4 consecutive integers because one of them would be divisible by 4 and therefore would not be product of distinct primes. There are several examples of 3 consecutive integers in this sequence. The first one is 33=3.11, 34=2.17, 35=5.7. - Matias Saucedo (solomatias(AT)yahoo.com.ar), Mar 15 2008
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REFERENCES
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D. A. Goldston, S. W. Graham, J. Pimtz and Y. Yildirim, "Small Gaps Between Primes or Almost Primes", arXiv:math.NT/0506067 v1, 3 2005.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Eric Weisstein's World of Mathematics, Semiprime
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FORMULA
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A002033(a(n))=3. - Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 26 2009
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MATHEMATICA
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Take[ Sort@ Flatten@ Table[Prime[m]*Prime[n], {n, 2, 26}, {m, n - 1}], 60] (Robert G. Wilson v (rgwv(at)rgwv.com), Dec 28 2005)
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PROGRAM
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(PARI) for(n=1, 214, if(bigomega(n)==2&&omega(n)==2, print1(n, ", "))) for(n=1, 214, if(bigomega(n)==2&&issquarefree(n), print1(n, ", ")))
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CROSSREFS
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Cf. A046386, A046387, A067885 (product of 4, 5 and 6 distinct primes, resp.)
Cf. A030229, A051709.
Cf. A001221 (omega(n)), A001222 (bigomega(n)), A001358 (semiprimes), A005117 (square-free), A007304 (square-free 3-almost primes).
Sequence in context: A000469 A120944 A052053 this_sequence A030229 A162730 A093772
Adjacent sequences: A006878 A006879 A006880 this_sequence A006882 A006883 A006884
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert P. Munafo (mrob(AT)mrob.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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