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A245392
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Sum_{k, k|n} 2^(k-1) + Sum_{1<=k<=n, gcd(k,n)=1} 2^(k-1).
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0
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2, 4, 8, 16, 32, 56, 128, 224, 480, 856, 2048, 3200, 8192, 13656, 29920, 54752, 131072, 202104, 524288, 857952, 1939168, 3495256, 8388608, 12918016, 33013248, 55924056, 124631008, 222655840, 536870912, 809850488, 2147483648, 3579172320, 7974270688, 14316557656
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OFFSET
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1,1
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COMMENTS
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The 1's in the binary expansion of 2^n - a(n) correspond to k such that 1 < gcd(k,n) < k < n. - Robert Israel, Jul 21 2014
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LINKS
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FORMULA
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If p is prime a(p) = 2^p.
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MAPLE
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f:= proc(k, n) local g; g:= igcd(k, n); g = 1 or g = k end proc:
A:= n -> 1 + add(2^(k-1), k=select(f, [$1..n], n));
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PROG
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(PARI) sum(k=1, n, if (gcd(k, n)==1, 2^(k-1), 0)) + sumdiv(n, k, k*2^(k-1));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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