login
A351116
Sum of the balanced numbers <= n.
1
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 31 2022
STATUS
approved