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

1,1

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.

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A005383, A099377, A099378, A109835.

Similar sequences: A023194, A048968, A074266, A348659.

Sequence in context: A328380 A256222 A258976 * A137162 A293863 A086769

Adjacent sequences: A348656 A348657 A348658 * A348660 A348661 A348662

Keyword

nonn

Author

Amiram Eldar, Oct 28 2021

Status

approved