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A009490
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Number of distinct orders of permutations of n objects; number of nonisomorphic cyclic subgroups of symmetric group S_n.
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9
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1, 1, 2, 3, 4, 6, 6, 9, 11, 14, 16, 20, 23, 27, 31, 35, 43, 47, 55, 61, 70, 78, 88, 98, 111, 123, 136, 152, 168, 187, 204, 225, 248, 271, 296, 325, 356, 387, 418, 455, 495, 537, 581, 629, 678, 732, 787, 851, 918, 986, 1056, 1133, 1217, 1307, 1399, 1498, 1600, 1708, 1823
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also number of different lcm's of partitions of n.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
Index entries for sequences related to lcm's
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FORMULA
| Sum(b(k), k=0..n), where b(k) is the number of partitions of k into distinct prime power parts (1 excluded) (A051613) - Vladeta Jovovic (vladeta(AT)eunet.rs)
G.f.: Prod(p prime, 1 + Sum(k >= 1, x^(p^k))) / (1-x) - David W. Wilson (davidwwilson(AT)comcast.net), Apr 19, 2000
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MATHEMATICA
| Table[ Length[ Union[ Apply[ LCM, Partitions[ n ], 1 ] ] ], {n, 30} ]
f[n_] := Length@ Union[LCM @@@ IntegerPartitions@ n]; Array[f, 60, 0]
(* Caution, the following is Extremely Slow and Resource Intensive *) CoefficientList[ Series[ Expand[ Product[1 + Sum[x^(Prime@ i^k), {k, 4}], {i, 10}]/(1 - x)], {x, 0, 30}], x]
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PROG
| (PARI) /* compute David W. Wilson's g.f., needs <1sec for 1000 terms */
N=1000; x='x+O('x^N); /* N terms */
gf=1; /* generating function */
{ forprime(p=2, N,
sm = 1; pp=p; /* sum; prime power */
while ( pp<N, sm += x^pp; pp *= p; );
gf *= sm; /* update g.f. */
); }
gf/=(1-x); /* cumulative sums */
Vec(gf) /* show terms */ /* From Joerg Arndt, Jan 19 2011 */
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CROSSREFS
| Cf. A051613, A000792, A000793, A034891.
Sequence in context: A073061 A006874 A034890 * A064778 A028335 A007464
Adjacent sequences: A009487 A009488 A009489 * A009491 A009492 A009493
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KEYWORD
| nonn,nice,easy
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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