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A261355
Numbers n such that the denominator of the harmonic mean of Omega(n) and tau(n) is prime.
1
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
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
Sequence in context: A064683 A317468 A329481 * A084384 A119885 A007964
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 15 2015
STATUS
approved