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Search: id:A007340
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| A007340 |
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Integer average divisor divides the number. Or, both harmonic and arithmetic means of divisors are integral.
(Formerly M4299)
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+0
4
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| 1, 6, 140, 270, 672, 1638, 2970, 6200, 8190, 18600, 18620, 27846, 30240, 32760, 55860, 105664, 117800, 167400, 173600, 237510, 242060, 332640, 360360, 539400, 695520, 726180, 753480, 1089270, 1421280, 1539720, 2229500, 2290260, 2457000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The following are also in A046985: 1,6,672,30240,32760. Also contains multiply perfect (A007691) numbers.
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REFERENCES
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G. L. Cohen, personal communication.
O. Ore, On the averages of the divisors of a number, Amer. Math. Monthly, 55 (1948), 615-619.
N. J. A. Sloane, Illustration for sequence M4299 (=A007340) in The Encyclopedia of Integer Sequences (with S. Plouffe), Academic Press, 1995.
D. Wells, Curious and interesting numbers, Penguin Books, p. 124.
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LINKS
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Hisanori Mishima, Factorizations of many number sequences
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FORMULA
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a=Sigma[ 1, x ]/Sigma[ 0, x ] integer and b=x/a also.
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EXAMPLE
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x=270: Sigma[ 0,270 ]=16, Sigma[ 1,270 ]=720; average divisor a=720/16=45 and integer 45 divides x, x/a=270/45=6, but 270 is not in A007691.
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MATHEMATICA
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Do[ a = DivisorSigma[0, n]/ DivisorSigma[1, n]; If[IntegerQ[n*a] && IntegerQ[1/a], Print[n]], {n, 1, 2500000}]
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CROSSREFS
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Intersection of A003601 and A001599. Cf. A007691, A046985 - A046987, A046999.
Sequence in context: A003994 A053467 A090944 this_sequence A122483 A123729 A123728
Adjacent sequences: A007337 A007338 A007339 this_sequence A007341 A007342 A007343
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KEYWORD
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nonn,nice
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AUTHOR
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njas
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EXTENSIONS
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Additional comments from Labos E. (labos(AT)ana.sote.hu)
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 03 2002
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