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

Author

Juri-Stepan Gerasimov, Dec 04 2009

Keywords

• nonn

Links

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

Crossrefs

Cf. A001221, A171182.

Programs

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 *)

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

Formula

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