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A138302
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Products of distinct relatively prime terms of A084400.
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0
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1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81
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OFFSET
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1,2
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COMMENTS
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These numbers are called "compact integers". They consist of 1 and the positive integers for which all exponents of primes in its prime power factorization are nonnegative powers of 2.
The density of this sequence exists and equals 0.872497...
There exist only seven compact factorials A000142(n) for n=1,2,3,6,7,10 and 11.
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REFERENCES
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V. Shevelev, Compact integers and factorials, Acta Arithmetica 126:3 (2007), pp. 195-236.
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LINKS
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Table of n, a(n) for n=1..72.
S. Litsyn and V. Shevelev, On Factorization of Integers with Restrictions on the Exponents, INTEGERS: The Electronic Journal of Combinatorial Number Theory 7 (2007), #A33.
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MATHEMATICA
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lst={}; Do[p=Prime[n]; s=p^(1/3); f=Floor[s]; a=f^3; d=p-a; AppendTo[lst, d], {n, 100}]; Union[lst] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)
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PROG
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(PARI) is(n)=if(n<8, n>0, vecmin(apply(n->n>>valuation(n, 2)==1, factor(n)[, 2]))) \\ Charles R Greathouse IV, Dec 07 2012
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CROSSREFS
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Cf. A084400, A050376, A005117.
Sequence in context: A007412 A220218 A096432 * A183220 A187947 A171524
Adjacent sequences: A138299 A138300 A138301 * A138303 A138304 A138305
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev, May 07 2008
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EXTENSIONS
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Incorrect comment removed by Charles R Greathouse IV, Dec 07 2012
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STATUS
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approved
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