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
Amiram Eldar, Table of n, a(n) for n = 1..10000
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
MATHEMATICA
Select[Range[100]^3, DivisorSigma[1, #] > 2# &] (* Amiram Eldar, Aug 14 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Dec 27 2006
EXTENSIONS
More terms from R. J. Mathar and Emeric Deutsch, Jan 07 2007
STATUS
approved