A061884 a(n) = Sum_{ d | n } phi(lcm(d,n/d)), where phi(n) = Euler totient A000010.

1, 2, 4, 5, 8, 8, 12, 12, 14, 16, 20, 20, 24, 24, 32, 26, 32, 28, 36, 40, 48, 40, 44, 48, 44, 48, 48, 60, 56, 64, 60, 56, 80, 64, 96, 70, 72, 72, 96, 96, 80, 96, 84, 100, 112, 88, 92, 104, 90, 88, 128, 120, 104, 96, 160, 144, 144, 112, 116, 160, 120, 120, 168, 116, 192

Offset: 1

Author

Vladeta Jovovic, May 12 2001

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000010, A001616, A057670, A007427.

Programs

Maple

A061884 := proc(n) local b,d: b := 0; for d from 1 to n do if irem(n,d)=0 then b := b+phi(lcm(d,n/d)); fi; od; RETURN(b); end:

Mathematica

Table[Plus @@ Map[ EulerPhi[LCM[ #, n/# ]] &, Select[ Range@n, (Mod[n, # ] == 0) &]], {n, 65}] (* Robert G. Wilson v, Sep 30 2006 *)

PARI

a(n)=sumdiv(n,d,eulerphi(lcm(d,n/d))) \\ Charles R Greathouse IV, Feb 21 2013