A182256 a(n) = 2^n - 2*n*A000048(n).

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

Offset: 0

Author

N. J. A. Sloane, Apr 21 2012

Keywords

• nonn

Comments

a(n) = total length of all cycles (see A000048) which are strictly less than the full length of 2n.

References

• R. K. Guy, Posting to Sequence Fans Mailing List, Apr 20 2012

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A000048.

Programs

Maple

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

Mathematica

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 *)