login
The odd part of Minkowski(n)/n!
0

%I #7 Jun 17 2019 14:09:14

%S 1,1,1,1,1,3,1,9,9,15,3,9,3,945,135,27,27,405,45,8505,1701,66825,6075,

%T 18225,6075,995085,76545,8505,1215,18225,1215,841995,841995,6506325,

%U 382725,32805,3645,850797675,44778825,3444525

%N The odd part of Minkowski(n)/n!

%F a(n) = A000265(A163176(n)). - _Michel Marcus_, Jun 17 2019

%p a := proc(n) local L,p;

%p L := proc(n,p,r) local q,s,m; m:=n-r; q:=p-r; s:=0;

%p do if q > n then break fi; s := s+iquo(m,q);

%p q := q*p od; s end; mul(p^(L(n,p,1)-L(n,p,0)),

%p p = select(isprime,[$3..n])); end

%t L[n_, p_, r_] := Module[{q, s, m}, m = n-r; q = p-r; s = 0; While[True, If[ q > n, Break[]]; s = s + Quotient[m, q]; q = q*p]; s];

%t a[n_] := Product[p^(L[n, p, 1]-L[n, p, 0]), {p, Select[Range[3, n], PrimeQ] }];

%t Table[a[n], {n, 0, 39}] (* _Jean-François Alcover_, Jun 17 2019 *)

%Y Cf. A000265, A053657, A163176.

%K nonn

%O 0,6

%A _Peter Luschny_, Jul 26 2009