A250094 Positive integers k such that the numerator of the harmonic mean of the divisors of k is equal to k.

1, 3, 5, 7, 11, 13, 17, 19, 20, 21, 22, 23, 27, 29, 31, 35, 37, 38, 39, 41, 43, 45, 47, 49, 53, 55, 56, 57, 59, 61, 65, 67, 68, 71, 73, 77, 79, 83, 85, 86, 89, 93, 97, 99, 101, 103, 107, 109, 110, 111, 113, 115, 116, 118, 119, 125, 127, 129, 131, 133, 134

Offset

1,2

Comments

A subsequence of A099377: n such that A099377(n) = n.

All odd primes are in this sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Colin Barker)

Example

20 is a term because the divisors of 20 are [1,2,4,5,10,20] and 6 / (1/1 + 1/2 + 1/4 + 1/5 + 1/10 + 1/20) = 20/7.

Mathematica

Select[Range[200], Numerator[HarmonicMean[Divisors[#]]]==#&] (* Harvey P. Dale, May 24 2017 *)
Select[Range[134], Numerator[DivisorSigma[0, #] * #/DivisorSigma[1, #]] == # &] (* Amiram Eldar, Mar 02 2020 *)

Prog

(PARI)
harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
s=[]; for(n=1, 500, if(numerator(harmonicmean(divisors(n)))==n, s=concat(s, n))); s

Crossrefs

Cf. A099377, A247081, A250095.

Sequence in context: A244365 A171014 A254050 * A351398 A285516 A319801

Adjacent sequences: A250091 A250092 A250093 * A250095 A250096 A250097

Keyword

nonn

Author

Colin Barker, Nov 12 2014

Status

approved