A261447 The number of distinct prime factors of the number of proper divisors of n.

0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1

Offset: 2

Author

R. J. Mathar, Aug 19 2015

Keywords

• nonn

Comments

Starts to differ from A174889 at n=64.

The first 2 occurs at n = 64, the first 3 at n = 1081080.

The first 4 occurs at n = 75424789440 and the first 5 occurs at 2474044411193114760000. - Charles R Greathouse IV, Aug 20 2015

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 2..10000
• L. Troupe, On the number of prime factors of values of the sum-of-proper-divisors function, J. Number Theory 150 (2015)120-135

Crossrefs

Cf. A001221, A032741, A007416, A002182.

Programs

Maple

A261447 := proc(n)
        A001221(A032741(n)) ;
end proc:

Mathematica

PrimeNu[DivisorSigma[0,#]-1&/@Range[2,82]] (* Ivan N. Ianakiev, Aug 20 2015 *)

PARI

a(n)=omega(numdiv(n)-1) \\ Charles R Greathouse IV, Aug 20 2015

Formula

a(n) = A001221(A032741(n)).