A160620 a(n) = Sum_{d|n} phi(n/d)^2*2^d.

0, 2, 6, 16, 28, 64, 96, 200, 320, 616, 1152, 2248, 4304, 8480, 16728, 33152, 66048, 131584, 263160, 524936, 1050176, 2098240, 4196952, 8389576, 16782976, 33555744, 67117920, 134220712, 268453360, 536872480, 1073780352, 2147485448, 4295034880, 8589944384

Offset: 0

Author

N. J. A. Sloane, Nov 21 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A053635.

Cf. A000079, A127473.

Programs

Maple

A160620 := proc(n)
    if n =0 then
        0;
    else
        add((numtheory[phi](n/d))^2*2^d,d=numtheory[divisors](n)) ;
    end if ;
end proc: # R. J. Mathar, Jun 24 2021

Mathematica

a[n_]:= If[n<1, 0, Sum[EulerPhi[n/d]^2 * 2^d, {d, Divisors[n]}]]; Table[a[n], {n,0,50}] (* G. C. Greubel, May 06 2018 *)

PARI

a(n) = if (n, sumdiv(n, d, eulerphi(n/d)^2*2^d), 0); \\ Michel Marcus, May 07 2018, Jun 22 2021

Formula

Dirichlet (convolution) product of A127473 and A000079. - R. J. Mathar, Jun 24 2021