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A210337
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Sum of distinct residues of all factorials mod 2^n.
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1
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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
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OFFSET
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0,3
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LINKS
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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