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A160258
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The entries of A033942, repeated for each different factorization into 3 factors larger than 1.
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1
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8, 12, 16, 18, 20, 24, 24, 27, 28, 30, 32, 32, 36, 36, 36, 40, 40, 42, 44, 45, 48, 48, 48, 48, 50, 52, 54, 54, 56, 56, 60, 60, 60, 60, 63, 64, 64, 64, 66, 68, 70, 72, 72, 72, 72, 72, 72, 75, 76, 78, 80, 80, 80, 80, 81, 84, 84, 84, 84, 88, 88, 90, 90, 90, 90, 92, 96, 96, 96, 96, 96, 96
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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This is the sequence of volumes for parallelepiped or rhombic hexahedron figurate numbers. Avoiding the use of 1 as a factor keeps from mentioning degenerate triples of the form 1*y*z or 1*1*z. This sequence lists products where only a volume expression will do.
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REFERENCES
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John H. Conway and Richard K. Guy, The book of numbers, Copernicus 1996, ISBN: 038797993X
Peter Pearce and Susan Pearce, Polyhedra primer, Van Nostrand Reinhold, 1978, ISBN 0442264968.
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LINKS
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EXAMPLE
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For n=1, its mention of 8 is the sole mention because 2*2*2 is the sole distinct producing triple for 8. 2*2*2 is the 1st possible triple not using 1.
At indices n=13 to 15, 3*3*4, 2*3*6, and 2*2*9 all give rise to 36.
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MAPLE
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A001222 := proc(n) numtheory[bigomega](n) ; end:
isA033942 := proc(n) RETURN(A001222(n) >= 3) ; end:
A160258rep := proc(a, minf) local c, d, f, ct ; c := [] ; for d in numtheory[divisors](a) do if d >= minf then if d = a then c := [op(c), [d]] ; ; else ct := A160258rep(a/d, d) ; for f in ct do c := [op(c), [d, op(f)] ] ; od: fi; fi; od: c; end:
A160258 := proc(a) local c, r, f ; c := 0 ; r := A160258rep(a, 2) ; for f in r do if nops(f) = 3 then c := c+1 ; fi; od: c ; end:
for n from 1 to 120 do if isA033942(n) then mu := A160258(n) ; for m from 1 to mu do printf("%d, ", n) ; od; fi; od: # R. J. Mathar, May 12 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 06 2009
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EXTENSIONS
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STATUS
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approved
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