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

2,63

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

Formula

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001221, A032741, A007416, A002182.

Sequence in context: A144411 A138253 A341969 * A287325 A336387 A358217

Adjacent sequences: A261444 A261445 A261446 * A261448 A261449 A261450

Keyword

nonn

Author

R. J. Mathar, Aug 19 2015

Status

approved