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

%I A210337 #22 Dec 15 2018 23:46:33
%S A210337 0,1,3,9,17,49,153,281,665,1433,3225,7705,17945,47641,64025,129561,
%T A210337 293401,752153,1341977,2914841,6421017,14547481,33421849,71170585,
%U A210337 138279449,247331353,645790233,1182661145,2558392857,5779618329,11685198361,23496358425
%N A210337 Sum of distinct residues of all factorials mod 2^n.
%H A210337 Alois P. Heinz, <a href="/A210337/b210337.txt">Table of n, a(n) for n = 0..1000</a>
%p A210337 a:= proc(n) local p, m, i, s;
%p A210337       p:= 2^n;
%p A210337       m:= 1;
%p A210337       s:= {};
%p A210337       for i to p while m<>0 do m:= m*i mod p; s:=s union {m} od;
%p A210337       add(i, i=s)
%p A210337     end:
%p A210337 seq (a(n), n=0..40);  # _Alois P. Heinz_, Mar 20 2012
%t A210337 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 *)
%o A210337 (PARI) nbf(n) = my(k=1); while(k! % 2^n, k++); k; \\ A007843
%o A210337 a(n) = my(nb=nbf(n)); vecsum(Set(vector(nb, k, k! % 2^n))); \\ _Michel Marcus_, Dec 15 2018
%Y A210337 Cf. A007843, A210184, A210185.
%K A210337 nonn
%O A210337 0,3
%A A210337 _Vladimir Shevelev_, Mar 20 2012
%E A210337 More terms from _Alois P. Heinz_, Mar 20 2012