A332270 - OEIS

%I #35 May 03 2021 02:13:44

%S 3,4,14,29,82,67117,86249,140064,185699,392081,2915083,6315155,

%T 9723681,17754993,820165642,9388829301,143904506919,192738887697

%N Numbers k such that Sum_{j=1..k} j*floor(k/j) is divisible by k+1.

%C a(19) > 5*10^11. - _Giovanni Resta_, May 05 2020

%t q[n_] := Divisible[Sum[j * Floor[n/j], {j, 1, n}], n + 1]; Select[Range[100], q] (* _Amiram Eldar_, May 03 2021 *)

%o (PARI) for(k=1, 1e4, if(sum(j=1, k, k\j*j)%(k+1)==0, print1(k", ")))

%o (PARI) s=0; for(k=1, 1e7, s+=sigma(k); if(s%(k+1)==0, print1(k", ")))

%Y Cf. A000203, A024916, A056550.

%K nonn,more

%O 1,1

%A _Seiichi Manyama_, May 04 2020

%E a(16)-a(18) from _Giovanni Resta_, May 05 2020