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A181950
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Weighted sum of all cyclic subgroups of the Alternating Group A_n.
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3
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1, 1, 4, 19, 91, 571, 4096, 38599, 370399, 3771751, 40020916, 486887611, 6457566259, 97397627419, 1566407932636, 25622476773391, 416792928270751, 7346982309720079, 141863542111338124, 2968348473040595971, 65223378275792128771, 1460499016109864574691, 32600807940657384926884
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OFFSET
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1,3
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COMMENTS
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Sum of the order of all cyclic subgroups of Alt_n.
Each permutation is counted as many times as it appears in a cyclic subgroup.
a(7) = 2^12 is remarkable as a power of 2.
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LINKS
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FORMULA
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EXAMPLE
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a(5) = 1*1 + 2*15 + 3*10 + 5*6 = 1 + 30 +30 +30 = 91.
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PROG
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(PARI) \\ permcount is number of permutations of given type.
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
a(n)={my(s=0); forpart(p=n, if(sum(i=1, #p, p[i]-1)%2==0, my(d=lcm(Vec(p))); s+=d*permcount(p)/eulerphi(d))); s} \\ Andrew Howroyd, Jul 03 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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