A348659 Numbers whose numerator and denominator of the harmonic mean of their divisors are both prime numbers.

3, 5, 13, 14, 15, 37, 42, 61, 66, 73, 92, 114, 157, 182, 193, 258, 277, 308, 313, 397, 402, 421, 457, 476, 477, 541, 546, 570, 613, 661, 673, 733, 744, 757, 812, 877, 978, 997, 1093, 1148, 1153, 1201, 1213, 1237, 1266, 1278, 1321, 1381, 1428, 1453, 1621, 1657

Offset: 1

Author

Amiram Eldar, Oct 28 2021

Keywords

• nonn

Comments

The prime terms of this sequence are the primes p such that (p+1)/2 is also a prime (A005383).

If p is in A109835, then p*(2*p-1) is a semiprime term.

Examples

			3 is a term since the harmonic mean of its divisors is 3/2 and both 2 and 3 are primes.
		

Links

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

Crossrefs

Cf. A005383, A099377, A099378, A109835.

Similar sequences: A023194, A048968, A074266, A348659.

Programs

Mathematica

q[n_] := Module[{h = DivisorSigma[0, n]/DivisorSigma[-1, n]}, And @@ PrimeQ[{Numerator[h], Denominator[h]}]]; Select[Range[2000], q]