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Number of distinct prime factors of n-th odd number.
5

%I #15 Sep 21 2024 08:42:08

%S 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,

%T 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,

%U 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

%N Number of distinct prime factors of n-th odd number.

%H Ray Chandler, <a href="/A092523/b092523.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OddNumber.html">Odd Number</a>.

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

%F 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

%t Table[PrimeNu[n],{n,1,211,2}] (* _Harvey P. Dale_, May 25 2015 *)

%o (PARI) a(n) = omega(2*n-1); \\ _Amiram Eldar_, Sep 21 2024

%Y Cf. A001221, A077761, A091304, A099812.

%K nonn,easy

%O 1,8

%A _Reinhard Zumkeller_, Apr 07 2004