cp's OEIS Frontend

A046999 Numbers k whose average divisor is nonintegral and divides k.

%I A046999 #23 Jun 08 2020 02:30:39
%S A046999 28,496,8128,950976,2178540,33550336,142990848,301953024,459818240,
%T A046999 675347400,714954240,995248800,1379454720,2701389600,3288789504,
%U A046999 6720569856,8589869056,10200236032,14254365440,30600708096,42763096320,43861478400,66433720320,71271827200
%N A046999 Numbers k whose average divisor is nonintegral and divides k.
%C A046999 The sequence contains perfect numbers (A000396) and others. Most of them have only small prime factors.
%C A046999 The first three terms are in A007691 (multiply perfect numbers) but 950976 is not since sigma_1/k is not an integer.
%C A046999 sigma_0(k) is the number of divisors of k (A000005).
%C A046999 sigma_1(k) is the sum of the divisors of k [same as sigma(k)] (A000203).
%C A046999 Harmonic numbers that are not arithmetic numbers. Of the 937 harmonic numbers below 10^14 there are just 90 such terms, of them 13 are multiply perfect numbers. - _Amiram Eldar_, Jun 08 2020
%H A046999 Amiram Eldar, <a href="/A046999/b046999.txt">Table of n, a(n) for n = 1..90</a> (terms below 10^14)
%F A046999 Average divisor = m = sigma_1(k)/sigma_0(k) is not an integer but k/m is.
%e A046999 k=28, sigma_0=6, sigma_1=56, m=sigma_1/sigma_0=9.333... is not an integer, but k/m=3 is;
%e A046999 k=950976, m=2958592/84=3521.333... but k/m=27 is integral.
%Y A046999 In A001599 but not in A003601.
%Y A046999 Cf. A007691, A046985, A046986, A046987, A000396.
%K A046999 nonn
%O A046999 1,1
%A A046999 _Labos Elemer_
%E A046999 More terms from _Jud McCranie_, Dec 25 2000
%E A046999 a(16)-a(24) from _Donovan Johnson_, Apr 22 2008