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A124581 Abundant cubes. 0
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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].

LINKS

Table of n, a(n) for n=1..33.

Christian Boyer, The smallest possible multiplicative magic squares.

EXAMPLE

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.

MAPLE

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, 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, Jan 10 2007

CROSSREFS

Cf. A111029 = magic products of 3 X 3 multiplicative magic squares.

Sequence in context: A250137 A109399 A111029 * A177493 A162142 A233859

Adjacent sequences:  A124578 A124579 A124580 * A124582 A124583 A124584

KEYWORD

nonn

AUTHOR

Tanya Khovanova, Dec 27 2006

EXTENSIONS

More terms from R. J. Mathar and Emeric Deutsch, Jan 07 2007

STATUS

approved

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Last modified July 23 05:58 EDT 2017. Contains 289686 sequences.