A210337 Sum of distinct residues of all factorials mod 2^n.

0, 1, 3, 9, 17, 49, 153, 281, 665, 1433, 3225, 7705, 17945, 47641, 64025, 129561, 293401, 752153, 1341977, 2914841, 6421017, 14547481, 33421849, 71170585, 138279449, 247331353, 645790233, 1182661145, 2558392857, 5779618329, 11685198361, 23496358425

Offset: 0

Author

Vladimir Shevelev, Mar 20 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007843, A210184, A210185.

Programs

Maple

a:= proc(n) local p, m, i, s;
      p:= 2^n;
      m:= 1;
      s:= {};
      for i to p while m<>0 do m:= m*i mod p; s:=s union {m} od;
      add(i, i=s)
    end:
seq (a(n), n=0..40);  # Alois P. Heinz, Mar 20 2012

Mathematica

a[n_] := Module[{k=0, s={}},  While[(r = Mod[k!, 2^n]) > 0, k++; AppendTo[s,r]]; Total@Union@s]; Array[a, 32, 0] (* Amiram Eldar, Dec 15 2018 *)

PARI

nbf(n) = my(k=1); while(k! % 2^n, k++); k; \\ A007843
a(n) = my(nb=nbf(n)); vecsum(Set(vector(nb, k, k! % 2^n))); \\ Michel Marcus, Dec 15 2018

Extensions

More terms from Alois P. Heinz, Mar 20 2012