A332270 Numbers k such that Sum_{j=1..k} j*floor(k/j) is divisible by k+1.

3, 4, 14, 29, 82, 67117, 86249, 140064, 185699, 392081, 2915083, 6315155, 9723681, 17754993, 820165642, 9388829301, 143904506919, 192738887697

Offset: 1

Author

Seiichi Manyama, May 04 2020

Keywords

• nonn
• more

Comments

a(19) > 5*10^11. - Giovanni Resta, May 05 2020

Crossrefs

Cf. A000203, A024916, A056550.

Programs

Mathematica

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

PARI

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

PARI

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

Extensions

a(16)-a(18) from Giovanni Resta, May 05 2020