A060179 Sum of distinct orders of degree-n permutations.

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

Offset: 0

Author

Vladeta Jovovic, Mar 19 2001

Keywords

• easy
• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A060014, A060015.

Cf. A009490.

Row sums of A256553.

Programs

Maple

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)):
seq(a(n), n=0..50);  # Alois P. Heinz, Jul 12 2017

Mathematica

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]];
a /@ Range[0, 50] (* Jean-François Alcover, Mar 14 2021, after Alois P. Heinz *)

Formula

G.f.: Prod(p prime, 1 + Sum(k >= 1, p^k*x^(p^k))) / (1-x). - Vladeta Jovovic, Sep 18 2002

Extensions

More terms from David Wasserman, May 29 2002

a(0)=1 prepended by Alois P. Heinz, Apr 01 2015