A053634 a(n) = Sum_{ d divides n } phi(d)*2^(n/d)/(2n).

2, 3, 4, 7, 10, 18, 30, 54, 94, 176, 316, 591, 1096, 2058, 3856, 7301, 13798, 26244, 49940, 95373, 182362, 349626, 671092, 1290714, 2485534, 4793790, 9256396, 17896284, 34636834, 67109898, 130150588, 252647064, 490853416, 954440950

Offset: 3

Author

N. J. A. Sloane, Mar 23 2000

Keywords

• nonn

Comments

Offset is 3 because a(2) is 3/2, not an integer. - Michel Marcus, Sep 11 2013

Links

• G. C. Greubel, Table of n, a(n) for n = 3..3000
• James East, Ron Niles, Integer polygons of given perimeter, arXiv:1710.11245 [math.CO], 2017.

Crossrefs

Cf. A000016, A000031, A053635, A063776.

Programs

Mathematica

a[n_] := DivisorSum[n, EulerPhi[#]*2^(n/#)&]/(2n); Table[a[n], {n, 3, 36}] (* Jean-François Alcover, Dec 07 2015 *)

PARI

a(n) = sumdiv (n, d, eulerphi(d)*2^(n/d)/(2*n));  \\ Michel Marcus, Sep 11 2013

Formula

a(n) = A000031(n)/2.