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Numbers k such that A099378(k) | (A099377(k) - 1).
3

%I #12 Nov 02 2021 15:59:34

%S 1,2,3,6,9,14,15,24,28,30,32,42,44,55,84,91,95,120,135,140,182,198,

%T 224,234,243,261,270,308,330,351,420,444,459,477,483,492,496,546,564,

%U 570,625,630,636,672,744,756,840,852,861,924

%N Numbers k such that A099378(k) | (A099377(k) - 1).

%C A disjoint union of the harmonic numbers (A001599) and the numbers whose harmonic mean of divisors is of the form m + 1/k, where m and k are integers.

%H Amiram Eldar, <a href="/A348865/b348865.txt">Table of n, a(n) for n = 1..10000</a>

%e 2 is a term since the harmonic mean of divisors of 2 is 4/3 and 3 | (4-1).

%t h[n_] := DivisorSigma[0, n]/DivisorSigma[-1, n]; q[n_] := Divisible[Numerator[(h1 = h[n])] - 1, Denominator[h1]]; Select[Range[1000], q]

%Y Cf. A001599, A099377, A099378, A348866.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 02 2021