A300668 a(n) = A000016(2*n).

1, 1, 2, 6, 16, 52, 172, 586, 2048, 7286, 26216, 95326, 349536, 1290556, 4793492, 17895736, 67108864, 252645136, 954437292, 3616814566, 13743895360, 52357696956, 199911205052, 764877654106, 2932031008768, 11258999068468, 43303842570872, 166799986203766, 643371375338656, 2484744621997516

Offset: 0

Author

Seiichi Manyama, Mar 10 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1667

Crossrefs

Cf. A000010 (phi), A000016, A300628.

Programs

Mathematica

a[n_] := DivisorSum[n, EulerPhi[#] * 4^(n/#) &, OddQ[#] &] / (4*n); a[0] = 1; Array[a, 30, 0] (* Amiram Eldar, Oct 04 2023 *)

PARI

a(n) = if (n==0, 1, sumdiv(n, d, if (d % 2, eulerphi(d)*4^(n/d)))/(4*n));  \\ Michel Marcus, Mar 11 2018

Formula

a(n) = (1/(4*n)) * Sum_{odd d divides n} phi(d)*4^(n/d) for n > 0.

a(n+1) = A300628(n,0).