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

Author

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

Keywords

• nonn

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.

Examples

			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.
		

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.

Programs

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

Extensions

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