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