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A023883 Nonprimes whose average of divisors is an integer.

%I A023883 #37 Feb 18 2024 02:02:46
%S A023883 1,6,14,15,20,21,22,27,30,33,35,38,39,42,44,45,46,49,51,54,55,56,57,
%T A023883 60,62,65,66,68,69,70,77,78,85,86,87,91,92,93,94,95,96,99,102,105,110,
%U A023883 111,114,115,116,118,119,123,125,126,129,132,133,134,135,138
%N A023883 Nonprimes whose average of divisors is an integer.
%C A023883 From _Bernard Schott_, Mar 27 2021: (Start)
%C A023883 Some subsequences of these nonprimes arithmetic numbers.
%C A023883   - Squares of primes of the form 6k+1 (A002476).
%C A023883   - Cubes of odd primes (A030078 \ {8}).
%C A023883   - Semiprimes 2*p where prime p is of the form 4k+3 (A002145).
%C A023883   - Semiprimes 3*p where p prime <> 3 (A001748 \ {9}).
%C A023883   - Integers 4*p where prime p is of the form 6k-1 (A007528). (End)
%H A023883 Amiram Eldar, <a href="/A023883/b023883.txt">Table of n, a(n) for n = 1..10000</a> (term 1..1000 from Paolo P. Lava)
%e A023883 Sigma(22) = 36, tau(22) = 4, sigma(22)/tau(2) = 9, 22 is not prime, hence 22 belongs to this sequence.
%t A023883 Select[{Mean[Divisors[#]], #}& /@ Select[Range[140], !PrimeQ[#]&], IntegerQ[#[[1]]]&][[All, 2]] (* _Jean-François Alcover_, Oct 31 2017 *)
%Y A023883 Intersection of A003601 and A018252.
%Y A023883 Equals A003601 \ A000040.
%Y A023883 Cf. A000005 (tau), A000203 (sigma).
%Y A023883 Cf. A001748, A002145, A002476, A007528, A030078.
%K A023883 nonn
%O A023883 1,2
%A A023883 _Olivier Gérard_