1,1

Also called sphenic numbers. All sphenic numbers have exactly three divisors. Moebius function of n is -1. Note the distinctions between this and "n has exactly three prime factors" or "n has exactly three distinct prime factors." The word "sphenic" also means "shaped like a wedge" [American Heritage Dictionary] as in dentation with "sphenic molars." - Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 11 2005

Also the volume of a sphenic brick. A sphenic brick is a rectangular parallelopiped whose sides are components of a sphenic number, namely whose sides are three distinct primes. Example: The distinct prime triple (3,5,7) produces a 3x5x7 unit brick which has volume 105 cubic units. 3-D analogue of 2-D A037074 Product of twin primes, per Cino Hilliard's comment. Compare with 3-D A107768 Golden 3-almost primes = Volumes of bricks (rectangular parallelopipeds) each of whose faces has golden semiprime area. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 08 2007

"Sphenic", The American Heritage Dictionary of the English Language, Fourth Edition, Houghton Mifflin Company, 2000.

T. D. Noe, Table of n, a(n) for n=1..10000

a:=proc(n) if bigomega(n)=3 and nops(factorset(n))=3 then n else fi end: seq(a(n), n=1..450); (Emeric Deutsch)

Union[Flatten[Table[Prime[n]*Prime[m]*Prime[k], {k, 20}, {n, k+1, 20}, {m, n+1, 20}]]]

Take[ Sort@ Flatten@ Table[ Prime@i Prime@j Prime@k, {i, 3, 21}, {j, 2, i - 1}, {k, j - 1}], 53] (* Robert G. Wilson v *)

Cf. A006881, A046386, A046387, A067885 (product of 2, 4, 5, and 6 distinct primes, resp.)

Cf. A046389, A046393, A061299, A067467, A071140, A096917, A096918, A096919, A100765, A103653, A107464.

Cf. A037074, A107768.

Sequence in context: A136152 A090815 A093599 this_sequence A053858 A075819 A034683

Adjacent sequences: A007301 A007302 A007303 this_sequence A007305 A007306 A007307

nonn

Simon Plouffe (plouffe(AT)math.uqam.ca)

More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 04 2006