A143275 A054525 * A029935.

1, 1, 3, 3, 7, 3, 11, 7, 12, 7, 19, 9, 23, 11, 21, 16, 31, 12, 35, 21, 33, 19, 43, 21, 48, 23, 44, 33, 55, 21, 59, 36, 57, 31, 77, 36, 71, 35, 69, 49, 79, 33, 83, 57, 84, 43, 91, 48, 108, 48, 93, 69, 103, 44, 133, 77, 105, 55, 115, 63, 119, 59, 132, 80, 161, 57, 131, 93, 129

Offset: 1

Author

Gary W. Adamson, Aug 03 2008

Keywords

• nonn
• easy
• mult

Examples

			a(4) = 3 = (0, -1, 0, 1) dot (1, 2, 4, 5) = (0 - 2 + 0 + 5), where K(0, -1, 0, 1) = row 4 of A054525 and A143275 = (1, 2, 4, 5, 8, 8, 12, ...).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A029935, A054525.

Programs

Maple

read("transforms") : A029935 := proc(n) local a,d ; a := 0 ; for d in numtheory[divisors](n) do a := a+ numtheory[phi](d)*numtheory[phi](n/d); od; RETURN(a) ; end: a029935 := [seq(A029935(n),n=1..300)] ; a143275 := MOBIUS(a029935) ; # R. J. Mathar, Jan 19 2009

Mathematica

f[p_, e_] := If[e > 1, (e*(p-1) + p + 2) * (p-1)^2 * p^(e-3), 2*p - 3]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 31 2023 *)

Formula

Möbius transform (A054525) of A029935: (1, 2, 4, 5, 8, 8, 12, 12, 16, ...).

Multiplicative with a(p) = 2*p - 3 and a(p^e) = (e*(p-1) + p + 2) * (p-1)^2 * p^(e-3) for e > 1. - Amiram Eldar, Aug 31 2023

Extensions

More terms from R. J. Mathar, Jan 19 2009