A261355 Numbers n such that the denominator of the harmonic mean of Omega(n) and tau(n) is prime.

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, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 77, 78, 79, 80, 82

Offset

1,1

Comments

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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.

Maple

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

Mathematica

Select[Range[100], PrimeQ[Denominator[2PrimeOmega[#]DivisorSigma[0, #]/(PrimeOmega[#] + DivisorSigma[0, #])]] &] (* Alonso del Arte, Aug 16 2015 *)

Crossrefs

Cf. A000005, A001222.

Sequence in context: A064683 A317468 A329481 * A084384 A119885 A007964

Adjacent sequences: A261352 A261353 A261354 * A261356 A261357 A261358

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 15 2015

Status

approved