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A060179
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Sum of distinct orders of degree-n permutations.
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4
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1, 1, 3, 6, 10, 21, 21, 50, 73, 116, 167, 248, 385, 496, 728, 959, 1548, 1899, 2835, 3609, 5042, 6403, 8336, 12187, 15522, 21358, 26090, 35298, 44147, 62512, 76289, 101403, 123883, 156880, 200086, 254175, 335380, 413184, 505860, 615258, 810767, 980747, 1293953
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: Prod(p prime, 1 + Sum(k >= 1, p^k*x^(p^k))) / (1-x). - Vladeta Jovovic, Sep 18 2002
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EXAMPLE
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Set of orders of all degree 7 permutations is {1,2,3,4,5,6,7,10,12) so a(7)=1+2+3+4+5+6+7+10+12=50.
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MAPLE
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b:= proc(n, i) option remember; (p->`if`(i*n=0, 1,
add(b(n-p^j, i-1)*p^j, j=1..ilog[p](n))+
b(n, i-1)))(`if`(i=0, 0, ithprime(i)))
end:
a:= n-> b(n, numtheory[pi](n)):
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MATHEMATICA
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b[n_, i_] := b[n, i] = Function [p, If[i*n == 0, 1, Sum[b[n-p^j, i-1]*p^j, {j, 1, Floor@Log[p, n]}] + b[n, i-1]]][If[i == 0, 0, Prime[i]]];
a[n_] := b[n, PrimePi[n]];
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CROSSREFS
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KEYWORD
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easy,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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