A092523 Number of distinct prime factors of n-th odd number.

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 3, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 3, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 3, 1, 1, 2, 2

Offset: 1

Author

Reinhard Zumkeller, Apr 07 2004

Keywords

• nonn
• easy

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Distinct Prime Factors.
• Eric Weisstein's World of Mathematics, Odd Number.

Crossrefs

Cf. A001221, A077761, A091304, A099812.

Programs

Mathematica

Table[PrimeNu[n],{n,1,211,2}] (* Harvey P. Dale, May 25 2015 *)

PARI

a(n) = omega(2*n-1); \\ Amiram Eldar, Sep 21 2024

Formula

a(n) = A001221(2*n-1).

Sum_{k=1..n} a(k) = n * (log(log(n)) + B - 1/2) + O(n/log(n)), where B is Mertens's constant (A077761). - Amiram Eldar, Sep 21 2024