A292786 a(n) = psi(n) - phi(n).

0, 2, 2, 4, 2, 10, 2, 8, 6, 14, 2, 20, 2, 18, 16, 16, 2, 30, 2, 28, 20, 26, 2, 40, 10, 30, 18, 36, 2, 64, 2, 32, 28, 38, 24, 60, 2, 42, 32, 56, 2, 84, 2, 52, 48, 50, 2, 80, 14, 70, 40, 60, 2, 90, 32, 72, 44, 62, 2, 128, 2, 66, 60, 64, 36, 124, 2, 76, 52, 120, 2, 120, 2, 78, 80, 84, 36, 144

Offset

1,2

Comments

Even numbers that are not the terms of this sequence are 12, 102, 114, 130, ...

Links

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

Formula

a(n) = A001615(n) - A000010(n).

a(n) = 2 iff n is prime.

a(n) = 2*A069359(n) iff n is in A070915.

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = 9/(2*Pi^2) = 0.455945... (A088245). - Amiram Eldar, Dec 05 2023

Mathematica

psi[n_] := If[n < 1, 0, n Sum[ MoebiusMu[d]^2/d, {d, Divisors@ n}]]; Array[psi@# - EulerPhi@# &, 87] (* Robert G. Wilson v, Sep 23 2017 *)

Prog

(PARI) a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1));
a(n) = a001615(n) - eulerphi(n); \\ after Charles R Greathouse IV at A001615

Crossrefs

Cf. A000010, A001615, A051612, A069359, A070915, A088245, A291784.

Sequence in context: A322671 A087909 A076078 * A326486 A357817 A053204

Adjacent sequences: A292783 A292784 A292785 * A292787 A292788 A292789

Keyword

nonn,easy,look

Author

Altug Alkan, Sep 23 2017

Status

approved