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A152444
n is included if the largest proper divisor of n that is coprime to d(n) is a composite, where d(n) is the total number of divisors of n.
2
16, 27, 30, 36, 42, 50, 54, 64, 66, 70, 75, 78, 81, 98, 100, 102, 105, 110, 114, 120, 125, 130, 135, 138, 140, 144, 147, 150, 154, 162, 165, 168, 170, 174, 175, 182, 186, 189, 190, 195, 196, 200, 210, 216, 220, 222, 225, 230, 231, 238, 242, 245, 246, 250, 255
OFFSET
1,1
COMMENTS
A152443(a(n)) is composite for all n.
EXAMPLE
There are 4 divisors of 27. These are 1,3,9,27. The proper divisors of 27 are therefore 1,3,9. The largest of these that is coprime to d(27) = 4 is 9. So a(27) = 9. (Note that in this case, the largest divisor of 27 coprime to 4 is 27, not 9.)
MATHEMATICA
a = {}; For[n = 2, n < 1000, n++, b = Max[Select[Drop[Divisors[n], -1], GCD[DivisorSigma[0, n], # ] == 1 &]]; If[b > 1 && ! PrimeQ[b], AppendTo[a, n]]]; a (* Stefan Steinerberger, Dec 06 2008 *)
CROSSREFS
Sequence in context: A038353 A043126 A043906 * A199013 A374007 A118642
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 04 2008
EXTENSIONS
Extended by Ray Chandler and Stefan Steinerberger, Dec 05 2008
STATUS
approved