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A144338
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Squarefree numbers > 1.
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2
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2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Nontrivial products of distinct primes. Sequence A005117 without the initial 1.
Also numbers n for which the following equation holds : (2^r)-sigma_0(p(1)*...*p(r)) = 0. This sequence describes the way RMS numbers (A140480) are grouped. In general if n = p(1)^alfa(1) *...* p(s)^alfa(s), alfa(i)>=1, we have the equation [2^sum_i=1..s{alfa(i)}] - sigma_0(p(1)^alfa(1) *...* p(s)^alfa(s)) = T. In terms of OEIS sequences the equation is : 2^(A001055(n)) - (A000005(n)) = T. This sequence has T=0, n=p(1)*...*p(r). If T=(2^k)-(k+1) then n=p^k. T splits the set of integers into subsets according to the form of prime factorization of the number n.
These can be computed with a modified Sieve of Eratosthenes: [1] start at n=2, [2] if (n is crossed out an even number of times) then (append n to the sequence and cross out all multiples of n), [3] set n:=n+1 and go to step 2; compare with the sieve for the complement of perfect powers in A007916. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 19 2009]
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LINKS
| S. R. Finch, Kalmar's Composition Constant, CiteSeer (2003).
Eric Weisstein's World of Math, Ordered Factorization
Index entries for sequences generated by sieves [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 19 2009]
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CROSSREFS
| Cf. A001055, A140480, A000005
Sequence in context: A193304 A076144 A005117 * A077377 A076786 A167171
Adjacent sequences: A144335 A144336 A144337 * A144339 A144340 A144341
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KEYWORD
| easy,nonn
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AUTHOR
| Ctibor O. Zizka (c.zizka(AT)email.cz), Sep 18 2008
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EXTENSIONS
| Corrected A-number typo. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 21 2009
Minor edits from Charles R Greathouse IV, Mar 18 2010
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