OFFSET
1,3
COMMENTS
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.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..50
FORMULA
EXAMPLE
a(5) = 1*1 + 2*15 + 3*10 + 5*6 = 1 + 30 +30 +30 = 91.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Olivier Gérard, Apr 03 2012
EXTENSIONS
Terms a(9) and beyond from Andrew Howroyd, Jul 03 2018
STATUS
approved