A261355 - OEIS

%I #28 Jul 30 2019 18:19:57

%S 2,3,4,5,6,7,8,9,10,11,13,14,15,17,19,21,22,23,24,25,26,27,29,30,31,

%T 32,33,34,35,36,37,38,39,40,41,42,43,46,47,48,49,51,53,54,55,56,57,58,

%U 59,61,62,64,65,66,67,69,70,71,72,73,74,77,78,79,80,82

%N Numbers n such that the denominator of the harmonic mean of Omega(n) and tau(n) is prime.

%C Here Omega(n) is the number of prime factors of n (with multiplicity), and tau(n) is the number of divisors of n. Thus this is the sequence of numbers n such that the denominator of 2 * Omega(n) * tau(n) / (Omega(n) + tau(n)) is prime.

%H Amiram Eldar, <a href="/A261355/b261355.txt">Table of n, a(n) for n = 1..10000</a>

%e For 24 we have Omega(24) = 4 and tau(24) = 8. Thus 2 * 4 * 8/(4 + 8) = 64/12 = 16/3, hence 24 is in the sequence.

%p with(numtheory): A261355 := n -> `if`(isprime(denom(2*bigomega(n)*tau(n)/ (bigomega(n)+tau(n)))), n, NULL): seq(A261355(n), n=1..100);

%t Select[Range[100], PrimeQ[Denominator[2PrimeOmega[#]DivisorSigma[0, #]/(PrimeOmega[#] + DivisorSigma[0, #])]] &] (* _Alonso del Arte_, Aug 16 2015 *)

%Y Cf. A000005, A001222.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Aug 15 2015