|
| |
|
|
A074064
|
|
Number of cycle types of degree-n permutations having the maximum possible order.
|
|
3
| |
|
|
1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 2, 3, 1, 1
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,6
|
|
|
FORMULA
| Coefficient of x^n in expansion of Sum_{i divides A000793(n)} mu(A000793(n)/i)*1/Product_{j divides i} (1-x^j).
|
|
|
EXAMPLE
| For n = 22 we have 4 such cycle types: [1, 1, 1, 3, 4, 5, 7], [1, 2, 3, 4, 5, 7], [3, 3, 4, 5, 7], [4, 5, 6, 7].
|
|
|
MAPLE
| A000793 := proc(n) option remember; local l, p, i ; l := 1: p := combinat[partition](n): for i from 1 to combinat[numbpart](n) do if ilcm( p[i][j] $ j=1..nops(p[i])) > l then l := ilcm( p[i][j] $ j=1..nops(p[i])) ; fi: od: RETURN(l) ; end proc:
taylInv := proc(i, n) local resul, j, idiv, k ; resul := 1 ; idiv := numtheory[divisors](i) ; for k from 1 to nops(idiv) do j := op(k, idiv) ; resul := resul*taylor(1/(1-x^j), x=0, n+1) ; resul := convert(taylor(resul, x=0, n+1), polynom) ; od ; coeftayl(resul, x=0, n) ; end proc:
A074064 := proc(n) local resul, a793, dvs, i, k ; resul := 0: a793 := A000793(n) ; dvs := numtheory[divisors](a793) ; for k from 1 to nops(dvs) do i := op(k, dvs) ; resul := resul+numtheory[mobius](a793/i)*taylInv(i, n) ; od : RETURN(resul) ; end proc: # R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 30 2007
|
|
|
CROSSREFS
| Cf. A000793, A074859.
Sequence in context: A136441 A030561 A202053 * A139549 A130782 A177706
Adjacent sequences: A074061 A074062 A074063 * A074065 A074066 A074067
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 15 2002
|
|
|
EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 30 2007
More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Oct 04 2011
|
| |
|
|
