A351561 a(n) = n + d(n) - phi(n), where d is the number of divisors function, and phi is the Euler totient function.

1, 3, 3, 5, 3, 8, 3, 8, 6, 10, 3, 14, 3, 12, 11, 13, 3, 18, 3, 18, 13, 16, 3, 24, 8, 18, 13, 22, 3, 30, 3, 22, 17, 22, 15, 33, 3, 24, 19, 32, 3, 38, 3, 30, 27, 28, 3, 42, 10, 36, 23, 34, 3, 44, 19, 40, 25, 34, 3, 56, 3, 36, 33, 39, 21, 54, 3, 42, 29, 54, 3, 60, 3, 42, 41, 46, 21, 62, 3, 58, 32, 46, 3, 72, 25, 48

Offset: 1

Author

Antti Karttunen, Feb 21 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000005, A000010 (phi), A008683 (mu), A020488 (fixed points), A051953, A063070.

Cf. also A055517.

Programs

Mathematica

Array[# + DivisorSigma[0, #] - EulerPhi[#] &, 86] (* Michael De Vlieger, Feb 21 2022 *)

PARI

A351561(n) = (n+numdiv(n)-eulerphi(n));

Formula

a(n) = A000005(n) + A051953(n) = n - A063070(n) = n + A000005(n) - A000010(n).

a(n) = Sum_{d|n} (1 + phi(d) - d*mu(n/d)). - Wesley Ivan Hurt, Jul 21 2025