A160258 The entries of A033942, repeated for each different factorization into 3 factors larger than 1.

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

Offset

1,1

Comments

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.

References

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.

Links

Table of n, a(n) for n=1..72.

Example

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.

Maple

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

Crossrefs

Sequence in context: A287373 A031034 A152758 * A071280 A033942 A111087

Adjacent sequences: A160255 A160256 A160257 * A160259 A160260 A160261

Keyword

nonn

Author

Chris G. Spies-Rusk (chaosorder4(AT)gmail.com), May 06 2009

Extensions

Edited and extended by R. J. Mathar, May 12 2009

Status

approved