A351116 Sum of the balanced numbers <= n.

1, 3, 6, 6, 6, 12, 12, 12, 12, 12, 12, 24, 24, 38, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 83, 83, 83, 83, 83, 118, 118, 118, 118, 118, 118, 118, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 216, 216, 216, 216, 216, 216, 216

Offset

1,2

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

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

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

Example

a(15) = 53; the sum of the balanced numbers <= 15 is 1+2+3+6+12+14+15 = 53.

Mathematica

f[n_] := n * Boole[Divisible[DivisorSigma[1, n], EulerPhi[n]]]; Accumulate @ Array[f, 100] (* Amiram Eldar, Feb 01 2022 *)
Accumulate[Table[If[Divisible[DivisorSigma[1, n], EulerPhi[n]], n, 0], {n, 70}]] (* Harvey P. Dale, May 09 2022 *)

Prog

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

Crossrefs

Cf. A000010 (phi), A000203 (sigma), A020492 (balanced numbers), A351114, A351115.

Sequence in context: A358548 A155067 A094011 * A295558 A295559 A161645

Adjacent sequences: A351113 A351114 A351115 * A351117 A351118 A351119

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 31 2022

Status

approved