A359954 a(n) = Sum_{d|n} tau(d)*phi(d)*mu(n/d).

1, 1, 3, 4, 7, 3, 11, 10, 14, 7, 19, 12, 23, 11, 21, 24, 31, 14, 35, 28, 33, 19, 43, 30, 52, 23, 54, 44, 55, 21, 59, 56, 57, 31, 77, 56, 71, 35, 69, 70, 79, 33, 83, 76, 98, 43, 91, 72, 114, 52, 93, 92, 103, 54, 133, 110, 105, 55, 115, 84, 119, 59, 154, 128, 161, 57, 131

Offset

1,3

Comments

Möbius transform of tau(n)*phi(n) (A062355).

Links

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

N. J. A. Sloane, Transforms

Formula

Multiplicative with a(p) = 2*p - 3 and a(p^e) = (e*p + p - e)*(p - 1)*p^(e - 2) for e > 1. - Amiram Eldar, May 16 2023

Mathematica

f[p_, e_] := If[e == 1, 2*p - 3, (e*p + p - e)*(p - 1)*p^(e - 2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 16 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, numdiv(d)*eulerphi(d)*moebius(n/d)); \\ Michel Marcus, May 13 2023

Crossrefs

Cf. A000005 (tau), A000010 (phi), A008683 (mu), A062355, A363012.

Sequence in context: A026248 A082089 A089961 * A316498 A200681 A161775

Adjacent sequences: A359951 A359952 A359953 * A359955 A359956 A359957

Keyword

nonn,easy,mult

Author

Wesley Ivan Hurt, May 12 2023

Status

approved