A070639 a(n) = (1/phi(n))*Sum_{k=1..n} phi(n*k).

1, 3, 5, 9, 11, 20, 19, 31, 33, 48, 43, 73, 59, 90, 88, 111, 97, 159, 121, 182, 165, 208, 173, 277, 211, 290, 263, 338, 271, 445, 309, 435, 396, 490, 414, 608, 433, 610, 544, 695, 531, 844, 585, 818, 745, 880, 697, 1080, 773, 1085, 918, 1126, 883, 1364, 995

Offset: 1

Author

Benoit Cloitre, May 13 2002

Keywords

• easy
• nonn
• look

Comments

a(2n)>a(2n+1) for n>=5.

If n is prime, a(n) = A002088(n)+1. - Robert Israel, Aug 10 2020

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A002088.

Programs

Maple

f:= n -> add(numtheory:-phi(n*k),k=1..n)/numtheory:-phi(n);
map(f, [$1..100]); # Robert Israel, Aug 10 2020

Mathematica

Table[1/EulerPhi[n]*Sum[EulerPhi[n*k],{k,n}],{n,60}] (* Harvey P. Dale, Dec 21 2015 *)

PARI

for(n=1,100,print1(sum(i=1,n,eulerphi(n*i))/eulerphi(n),","))