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A182256
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a(n) = 2^n - 2*n*A000048(n).
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1
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1, 0, 0, 2, 0, 2, 4, 2, 0, 8, 4, 2, 16, 2, 4, 38, 0, 2, 64, 2, 16, 134, 4, 2, 256, 32, 4, 512, 16, 2, 1084, 2, 0, 2054, 4, 158, 4096, 2, 4, 8198, 256, 2, 16444, 2, 16, 33272, 4, 2, 65536, 128, 1024, 131078, 16, 2, 262144, 2078, 256, 524294, 4, 2, 1052656, 2, 4, 2097656, 0, 8222, 4194364, 2, 16, 8388614, 17404, 2, 16777216, 2, 4, 33587168, 16, 2174, 67108924
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OFFSET
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0,4
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COMMENTS
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a(n) = total length of all cycles (see A000048) which are strictly less than the full length of 2n.
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REFERENCES
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R. K. Guy, Posting to Sequence Fans Mailing List, Apr 20 2012
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..2000
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MAPLE
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with (numtheory):
a:= n-> 2^n -add (mobius(d)*2^(n/d), d=select(x->is(x, odd), divisors(n))):
seq (a(n), n=0..80); # Alois P. Heinz, Apr 21 2012
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MATHEMATICA
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a[n_] := 2^n - DivisorSum[n, Mod[#, 2]*MoebiusMu[#]*2^(n/#)&]; a[0] = 1;
Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Mar 27 2017 *)
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CROSSREFS
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Cf. A000048.
Sequence in context: A037036 A055947 A015910 * A164993 A305572 A223487
Adjacent sequences: A182253 A182254 A182255 * A182257 A182258 A182259
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Apr 21 2012
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STATUS
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approved
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