cp's OEIS Frontend

A060179 Sum of distinct orders of degree-n permutations.

%I A060179 #24 Aug 17 2024 03:24:52
%S A060179 1,1,3,6,10,21,21,50,73,116,167,248,385,496,728,959,1548,1899,2835,
%T A060179 3609,5042,6403,8336,12187,15522,21358,26090,35298,44147,62512,76289,
%U A060179 101403,123883,156880,200086,254175,335380,413184,505860,615258,810767,980747,1293953
%N A060179 Sum of distinct orders of degree-n permutations.
%H A060179 Alois P. Heinz, <a href="/A060179/b060179.txt">Table of n, a(n) for n = 0..10000</a>
%F A060179 G.f.: Prod(p prime, 1 + Sum(k >= 1, p^k*x^(p^k))) / (1-x). - _Vladeta Jovovic_, Sep 18 2002
%e A060179 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.
%p A060179 b:= proc(n, i) option remember; (p->`if`(i*n=0, 1,
%p A060179        add(b(n-p^j, i-1)*p^j, j=1..ilog[p](n))+
%p A060179          b(n, i-1)))(`if`(i=0, 0, ithprime(i)))
%p A060179     end:
%p A060179 a:= n-> b(n, numtheory[pi](n)):
%p A060179 seq(a(n), n=0..50);  # _Alois P. Heinz_, Jul 12 2017
%t A060179 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]]];
%t A060179 a[n_] := b[n, PrimePi[n]];
%t A060179 a /@ Range[0, 50] (* _Jean-François Alcover_, Mar 14 2021, after _Alois P. Heinz_ *)
%Y A060179 Cf. A060014, A060015.
%Y A060179 Cf. A009490.
%Y A060179 Row sums of A256553.
%K A060179 easy,nonn
%O A060179 0,3
%A A060179 _Vladeta Jovovic_, Mar 19 2001
%E A060179 More terms from _David Wasserman_, May 29 2002
%E A060179 a(0)=1 prepended by _Alois P. Heinz_, Apr 01 2015