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A120065
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Number of permutations on 1..n where gcd(s_i,n) = gcd(i,n). Also product phi(d)! ; d divides n.
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1
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1, 1, 2, 2, 24, 4, 720, 48, 1440, 576, 3628800, 192, 479001600, 518400, 1935360, 1935360, 20922789888000, 2073600, 6402373705728000, 46448640, 689762304000, 13168189440000, 1124000727777607680000, 185794560, 58389648196239360000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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EXAMPLE
| a(8) = 48 = 4! * 2! * 1! * 1! because we can permute [1,3,5,7] in 4! ways, [2,6] in 2! ways and 4 and 8 are fixed.
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PROG
| (PARI) a(n) = prod(i=1, n, if(n%i==0, eulerphi(i)!, 1))
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CROSSREFS
| Cf. A029940 Product phi(d); d divides n. A000010 Euler totient function phi(n).
Sequence in context: A093355 A122962 A048648 * A131448 A156447 A127261
Adjacent sequences: A120062 A120063 A120064 * A120066 A120067 A120068
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KEYWORD
| nonn
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AUTHOR
| Martin Fuller (martin_n_fuller(AT)btinternet.com), Jun 06 2006
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