A078120 Number of distinct prime divisors of n-th balanced number.

0, 1, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 4, 5, 4, 4, 4, 3, 3, 4, 4, 3, 2, 4, 4, 4, 4, 3, 4, 3, 4, 4, 5, 4, 4, 4, 3, 4, 3, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 3, 4, 5, 4, 5, 5, 4, 5, 4, 4, 4, 5, 4, 4, 5, 4, 4, 3, 5, 5, 4, 4, 5, 4, 4

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A001221(A020492(n)).

Example

The 575th balanced number is 2089542 = 2*3*7*13*43*89, so a(575)=6; sigma(2089542)/phi(2089542) = 10.

Mathematica

PrimeNu /@ Select[Range[10^5], Divisible[DivisorSigma[1, #], EulerPhi[#]] &] (* Amiram Eldar, Dec 05 2019 *)

Crossrefs

Cf. A020492, A001221.

Sequence in context: A163374 A108502 A260235 * A057525 A331362 A139325

Adjacent sequences: A078117 A078118 A078119 * A078121 A078122 A078123

Keyword

nonn

Author

Labos Elemer, Dec 06 2002

Status

approved