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A250095
Positive integers k such that the numerator of the harmonic mean of the proper divisors of k is equal to k.
3
4, 27, 28, 54, 56, 64, 68, 91, 99, 100, 133, 138, 148, 154, 165, 188, 217, 222, 247, 259, 268, 276, 279, 290, 301, 308, 369, 375, 388, 403, 414, 427, 428, 430, 469, 474, 481, 508, 511, 540, 544, 548, 549, 553, 559, 589, 609, 621, 627, 628, 639, 642, 665, 668
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Colin Barker)
EXAMPLE
27 is a term because the proper divisors of 27 are [1,3,9] and 3 / (1/1 + 1/3 + 1/9) = 27/13.
MATHEMATICA
Select[Range[668], CompositeQ[#] && Numerator[(DivisorSigma[0, #] - 1) * #/(DivisorSigma[1, #] - 1)] == # &] (* Amiram Eldar, Mar 02 2020 *)
PROG
(PARI)
harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
properdivisors(n) = d=divisors(n); vector(#d-1, k, d[k])
s=[]; for(n=2, 1000, if(numerator(harmonicmean(properdivisors(n)))==n, s=concat(s, n))); s
CROSSREFS
Sequence in context: A176031 A093845 A351747 * A085702 A068349 A129204
KEYWORD
nonn
AUTHOR
Colin Barker, Nov 12 2014
STATUS
approved