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A109813
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Number of permutations of (the positive integers <= n and coprime to n), where each element of the permutations is coprime to its adjacent elements.
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1
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1, 1, 2, 2, 12, 2, 72, 24, 144, 12, 22032, 24, 476928, 480, 1728, 9600, 805146624, 720, 36481536000, 30240, 1728000, 312000, 192859121664000, 40320, 2159795404800, 46293120, 249684249600, 58423680
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Sequence continues: a(29) = ?, 40320, ?, 1893397524480, 32006016000000, 478511953920, ?, 209018880, ?, 122634632171520, ?, 665481277440, ?, 399168000. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 25 2006
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EXAMPLE
| The integers coprime to 10 and <= 10 are (1,3,7,9).
Of the permutations of these integers, there are 12 permutations where all adjacent terms are coprime, ie where 3 and 9 are not adjacent. So the 10th term of the sequence is 12.
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PROG
| (PARI) {A109813(x)=local(v, A, d, r, M, i, j); n=eulerphi(x); v=vector(n, i, 0); j=0; for(i=1, x, if(gcd(i, x)==1, j++; v[j]=i)); A=matrix(n, n, i, j, gcd(v[i], v[j])==1); r=0; for(s=1, 2^n-1, M=vecextract(A, s, s)^(n-1); d=matsize(M)[1]; r+=(-1)^(n-d)*sum(i=1, d, sum(j=1, d, M[i, j]))); r} - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 25 2006
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CROSSREFS
| Cf. A076220.
Sequence in context: A076976 A058044 A128269 * A086595 A013605 A073768
Adjacent sequences: A109810 A109811 A109812 * A109814 A109815 A109816
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KEYWORD
| more,nonn
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AUTHOR
| Leroy Quet Aug 16 2005
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EXTENSIONS
| More terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 25 2006
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