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A348825
Numbers k such that the denominator of the harmonic mean of the divisors of k is larger than k.
3
2, 4, 8, 9, 16, 25, 36, 64, 80, 81, 100, 104, 121, 128, 144, 208, 225, 256, 272, 289, 320, 324, 400, 484, 512, 529, 576, 625, 729, 841, 900, 1024, 1088, 1089, 1156, 1250, 1296, 1300, 1332, 1575, 1600, 1664, 1681, 1856, 1936, 2025, 2116, 2196, 2209, 2304, 2368
OFFSET
1,1
COMMENTS
Numbers k such that A099378(k) > k.
This sequence is infinite. For example, if p is a prime of the form 6*k-1, then p^2 is a term.
2 is the only prime term, since the denominator of the harmonic mean of the divisors of an odd prime p is (p+1)/2 < p.
LINKS
EXAMPLE
2 is a term since the harmonic mean of the divisors of 2 is 4/3 and 3 > 2.
4 is a term since the harmonic mean of the divisors of 4 is 12/7 and 7 > 4.
MATHEMATICA
q[n_] := Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]] > n; Select[Range[2500], q]
PROG
(PARI) isok(k) = my(d=divisors(k)); (denominator(#d/sum(i=1, #d, 1/d[i])) > k); \\ Michel Marcus, Nov 01 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 01 2021
STATUS
approved