A351115 Number of balanced numbers <= n.

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13

Offset

1,2

Comments

A balanced number k is a number such that phi(k) | sigma(k).

Links

Table of n, a(n) for n=1..80.

Formula

a(n) = Sum_{k<=n, phi(k)|sigma(k)} 1.

a(n) = Sum_{k=1..n} c(k), where c is the characteristic function of balanced numbers (A351114).

Example

a(15) = 7; the 7 balanced numbers <= 15 are 1,2,3,6,12,14,15.

Mathematica

f[n_] := Boole[Divisible[DivisorSigma[1, n], EulerPhi[n]]]; Accumulate @ Array[f, 100] (* Amiram Eldar, Feb 01 2022 *)

Prog

(PARI) a(n) = sum(k=1, n, if (!(sigma(k) % eulerphi(k)), 1)); \\ Michel Marcus, Feb 01 2022

Crossrefs

Cf. A000010 (phi), A000203 (sigma), A020492 (balanced numbers), A351114.

Sequence in context: A194847 A262070 A117806 * A085423 A260998 A361110

Adjacent sequences: A351112 A351113 A351114 * A351116 A351117 A351118

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 31 2022

Status

approved