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Search: id:A121382
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| A121382 |
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Number of ways of writing n as pqr, with p<=q<=r and (p,q)=(q,r)=1. |
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2
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| 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 2, 1, 5, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 5, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 7, 1, 2, 2, 1, 2, 5, 1, 2, 2, 5, 1, 2, 1, 2, 2, 2, 2, 5, 1, 3, 1, 2, 1, 6, 2, 2, 2, 2, 1, 6, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 5, 1, 2, 5
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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3-factor analogue of A007875 Number of ways of writing n as pq, with p<=q, (p,q)=1.
a(n) = 1 iff n is a power prime (A000961).
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EXAMPLE
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a(4) = 1 because 4 = 1*1*4.
a(6) = 2 because 6 = 1*1*6 = 1*2*3.
a(24) = 3 because 24 = 1*1*24 = 1*3*8 = 2*3*4.
a(30) = 5 because 30 = 1*1*30 = 1*2*15 = 1*3*10 = 1*5*6 = 2*3*5.
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MATHEMATICA
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f[n_] := Block[{d = Divisors@n, m = DivisorSigma[0, n], s = {}}, If[m == 2, 1, Do[ AppendTo[s, {d[[p]], d[[q]], d[[r]]}], {r, m}, {q, r}, {p, q}]; Length@ Select[s, Times @@ # == n && GCD[ #[[1]], #[[2]]] == GCD[ #[[2]], #[[3]]] == 1 &]]]; Array[f, 105] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000040, A001248, A001358, A007304, A007875, A030078.
First occurrence of k: A122829.
Sequence in context: A096825 A007875 A050320 this_sequence A051265 A008647 A036475
Adjacent sequences: A121379 A121380 A121381 this_sequence A121383 A121384 A121385
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 06 2006
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EXTENSIONS
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Edited, corrected and extended by Robert G. Wilson v Sep 11 2006
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