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A060179 Sum of distinct orders of degree-n permutations. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A060014, A060015.

Cf. A009490.

Row sums of A256553.

Sequence in context: A122628 A343386 A068865 * A056411 A068855 A068882

Adjacent sequences:  A060176 A060177 A060178 * A060180 A060181 A060182

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Mar 19 2001

EXTENSIONS

More terms from David Wasserman, May 29 2002

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

STATUS

approved

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Last modified September 26 17:27 EDT 2022. Contains 357000 sequences. (Running on oeis4.)