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Search: id:A124581
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| 216, 1000, 1728, 2744, 5832, 8000, 10648, 13824, 17576, 21952, 27000, 46656, 64000, 74088, 85184, 110592, 125000, 140608, 157464, 175616, 216000, 287496, 314432, 343000, 373248, 438976, 474552, 512000, 592704, 681472, 729000, 778688, 884736
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Abundant cubes can't be prime powers for obvious reasons. Hence all these numbers can be represented as a^3*b^3 for some coprime a and b. a^3*b^3 is the magic product of the following magic 3 X 3 multiplicative square: [a*b^2, 1, a^2*b; a^2, ab, b^2; b, a^2*b^2; a].
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LINKS
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Christian Boyer, The smallest possible multiplicative magic squares.
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EXAMPLE
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216 is in the sequence because 216=6^3 and the sum of the proper divisors of 216 is 108+72+54+...+3+2+1 > 216.
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MAPLE
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isA005101 := proc(n) if numtheory[sigma](n) > 2*n then RETURN(true) ; else RETURN(false) ; fi ; end : for n from 1 to 120 do if isA005101(n^3) then printf("%d, ", n^3) ; fi ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 07 2007
with(numtheory): a:=proc(n) if sigma(n^3)>2*n^3 then n^3 else fi end: seq(a(n), n=1..110); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 10 2007
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CROSSREFS
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Cf. A111029 = magic products of 3 X 3 multiplicative magic squares.
Sequence in context: A066890 A135590 A111029 this_sequence A162142 A016863 A033698
Adjacent sequences: A124578 A124579 A124580 this_sequence A124582 A124583 A124584
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KEYWORD
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nonn
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AUTHOR
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Tanya Khovanova (tanyakh(AT)yahoo.com), Dec 27 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 07 2007
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