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A218464 Numbers m = (Sum_(j=1..k) tau(j)) with m divisible by k, where tau(j) is the number of divisors of j.

%I A218464 #22 Feb 14 2021 15:29:12
%S A218464 1,8,10,45,168,176,188,605,2016,2040,2082,6510,20384,62433,62523,
%T A218464 564542,4928261,4928703,4928729,42018075,351871865,1012753620,
%U A218464 1012755546,2905896480,2905898228,192057921660,1542529159875,12309661243665,12309661255437,34700429419432
%N A218464 Numbers m = (Sum_(j=1..k) tau(j)) with m divisible by k, where tau(j) is the number of divisors of j.
%C A218464 See A050226 for the values of k. - _T. D. Noe_, Mar 27 2013
%H A218464 Giovanni Resta, <a href="/A218464/b218464.txt">Table of n, a(n) for n = 1..39</a> (based on A050226 values)
%e A218464 10 is in sequence because k=5 divides the sum of tau(1) + tau(2) + tau(3) + tau(4) + tau(5) = 1+2+2+3+2 = 10.
%p A218464 with(numtheory);
%p A218464 A218464:=proc(q)  local n;  a:=0;
%p A218464 for n from 1 to q do a:=a+tau(n) if type(a/n,integer) then print(a); fi; od; end:
%p A218464 A218464 (10^10); # _Paolo P. Lava_, Mar 26 2013
%t A218464 sm = 0; t = {}; Do[sm = sm + DivisorSigma[0, n]; If[Mod[sm, n] == 0, AppendTo[t, sm]], {n, 1000}]; t (* _T. D. Noe_, Mar 27 2013 *)
%Y A218464 Cf. A000005, A168133.
%Y A218464 Cf. A050226 (has the values of k).
%K A218464 nonn
%O A218464 1,2
%A A218464 _Paolo P. Lava_, Mar 26 2013
%E A218464 a(22)-a(30) from _Giovanni Resta_, Mar 28 2013