A171157 Number of distinct primes > 3 that divide n.

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

Offset

1,35

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A001221(n) - A171182(n).

Maple

omega := proc(n) nops(numtheory[factorset](n)) ; end proc:
A171182 := proc(n) op(1+ (n mod 6), [2, 0, 1, 1, 1, 0]) ; end proc:
A171157 := proc(n) omega(n)-A171182(n) ; end proc: seq(A171157(n), n=1..120) ; # R. J. Mathar, Dec 09 2009

Mathematica

Table[PrimeNu[n] - (5 + 3*Cos[n*Pi] + 4*Cos[2*n*Pi/3])/6, {n, 1, 100}] (* G. C. Greubel, May 16 2017 *)
Table[Count[FactorInteger[n][[;; , 1]], _?(#>3&)], {n, 110}] (* Harvey P. Dale, Nov 16 2024 *)

Prog

(PARI) for(n=1, 100, print1(round(omega(n) - (5 + 3*cos(n*Pi) + 4*cos(2*n*Pi/3))/6), ", ")) \\ G. C. Greubel, May 16 2017

Crossrefs

Cf. A001221, A171182.

Sequence in context: A228085 A154782 A265196 * A194301 A194341 A171905

Adjacent sequences: A171154 A171155 A171156 * A171158 A171159 A171160

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 04 2009

Status

approved