A319341 a(n) = A000010(n) - A173557(n).

0, 0, 0, 1, 0, 0, 0, 3, 4, 0, 0, 2, 0, 0, 0, 7, 0, 4, 0, 4, 0, 0, 0, 6, 16, 0, 16, 6, 0, 0, 0, 15, 0, 0, 0, 10, 0, 0, 0, 12, 0, 0, 0, 10, 16, 0, 0, 14, 36, 16, 0, 12, 0, 16, 0, 18, 0, 0, 0, 8, 0, 0, 24, 31, 0, 0, 0, 16, 0, 0, 0, 22, 0, 0, 32, 18, 0, 0, 0, 28, 52, 0, 0, 12, 0, 0, 0, 30, 0, 16, 0, 22, 0, 0, 0, 30, 0, 36, 40, 36, 0, 0, 0, 36, 0

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A000010(n) - A173557(n).

a(n) = A318841(n) - A051953(n).

a(A005117(n)) = 0. - Ivan N. Ianakiev, Sep 18 2018

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A059956 - A307868 = 0.136246... . - Amiram Eldar, Dec 21 2023

Mathematica

a[n_] := EulerPhi[n] - Times @@ (FactorInteger[n][[;; , 1]] - 1); a[1] = 0; Array[a, 100] (* Amiram Eldar, Dec 21 2023 *)

Prog

(PARI)
A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
A319341(n) = (eulerphi(n)-A173557(n));

Crossrefs

Cf. A000010, A051953, A173557, A318841, A319340, A126864.

Cf. A013661, A307868.

Sequence in context: A025120 A025096 A261137 * A086798 A155061 A322016

Adjacent sequences: A319338 A319339 A319340 * A319342 A319343 A319344

Keyword

nonn,easy

Author

Antti Karttunen, Sep 17 2018

Status

approved