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A034836
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Number of ways to write n as n = x*y*z with 1<=x<=y<=z<=n.
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21
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1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 4, 1, 4, 1, 4, 2, 2, 1, 6, 2, 2, 3, 4, 1, 5, 1, 5, 2, 2, 2, 8, 1, 2, 2, 6, 1, 5, 1, 4, 4, 2, 1, 9, 2, 4, 2, 4, 1, 6, 2, 6, 2, 2, 1, 10, 1, 2, 4, 7, 2, 5, 1, 4, 2, 5, 1, 12, 1, 2, 4, 4, 2, 5, 1, 9, 4, 2, 1, 10, 2, 2, 2, 6, 1, 10, 2, 4, 2, 2, 2, 12, 1, 4, 4, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Number of boxes with integer edge lengths and volume n.
Starts the same as, but is different from, A033273. First values of n such that a(n) differs from A033273(n) are 36,48,60,64,72,80,84,90,96,100 - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 25 2002
a(n) depends only on the signature of n; the sorted exponents of n. For instance, a(12) and a(18) are the same because both 12 and 18 have signature (1,2). - T. D. Noe, Nov 02 2011
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
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EXAMPLE
| a(12)=4 because we can write 12=1*1*12=1*2*6=1*3*4=2*2*3
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MAPLE
| f:=proc(n) local t1, i, j, k; t1:=0; for i from 1 to n do for j from i to n do for k from j to n do if i*j*k = n then t1:=t1+1; fi; od: od: od: t1; end;
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PROG
| (PARI) A038548(n)=if(n>=0, sumdiv(n, d, d*d<=n)) /* <== rhs from A038548 (Michael Somos) */ a(n)=if(n>=0, sumdiv(n, d, if(d^3<=n, A038548(n/d) - sumdiv(n/d, d0, d0<d)))) - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 27 2006
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CROSSREFS
| See also: writing n = x*y (A038548, unordered, A000005, ordered), n = x*y*z (this sequence, unordered, A007425, ordered), n = w*x*y*z (A007426, ordered)
Cf. A088432, A088433, A088434.
Sequence in context: A069157 A076526 A033273 * A001055 A129138 A112970
Adjacent sequences: A034833 A034834 A034835 * A034837 A034838 A034839
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KEYWORD
| nonn
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AUTHOR
| Erich Friedman (erich.friedman(AT)stetson.edu)
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