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A247081
Positive integers k such that the numerator of the harmonic mean of the nontrivial divisors of k is equal to k.
3
8, 15, 18, 21, 33, 35, 39, 45, 51, 55, 57, 63, 65, 69, 77, 81, 85, 87, 91, 93, 95, 99, 111, 115, 117, 119, 123, 128, 129, 133, 141, 143, 145, 147, 153, 155, 159, 161, 162, 171, 175, 177, 183, 185, 187, 201, 203, 205, 207, 209, 213, 215, 217, 219, 221, 235
OFFSET
1,1
COMMENTS
No primes are in this sequence.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Colin Barker)
EXAMPLE
18 is a term because the nontrivial divisors of 18 are [2,3,6,9] and 4 / (1/2 + 1/3 + 1/6 + 1/9) = 18/5.
MATHEMATICA
Select[Range[235], CompositeQ[#] && Numerator[(DivisorSigma[0, #] - 2) * #/(DivisorSigma[1, #] - # -1)] == # &] (* Amiram Eldar, Mar 02 2020 *)
PROG
(PARI)
harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
nontrivialdivisors(n) = d=divisors(n); vector(#d-2, k, d[k+1])
s=[]; for(n=2, 500, t=nontrivialdivisors(n); if(#t>0 && numerator(harmonicmean(t))==n, s=concat(s, n))); s
CROSSREFS
Sequence in context: A179107 A160524 A161541 * A133157 A014544 A237610
KEYWORD
nonn
AUTHOR
Colin Barker, Nov 17 2014
STATUS
approved