A078120 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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