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

0,4

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

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 *)

Crossrefs

Cf. A000048.

Sequence in context: A037036 A055947 A015910 * A164993 A305572 A223487

Adjacent sequences: A182253 A182254 A182255 * A182257 A182258 A182259

Keyword

nonn

Author

N. J. A. Sloane, Apr 21 2012

Status

approved