A088825 Numbers n such that the sum of largest prime factors of numbers from 1 to n is divisible by n.

1, 2, 8, 9, 32, 62, 558, 993, 995, 1947, 2150, 4343, 9944, 10977, 43054658, 202275890, 2291937393, 2459073795, 2836929091, 3737529738, 21382629569, 248208997602, 389691028017, 838566394212, 1019000924619

Offset: 1

Author

Labos Elemer, Oct 22 2003

Keywords

• nonn

Comments

a(21) > 15*10^9. - Donovan Johnson, Nov 01 2009

a(22) > 10^11. - Donovan Johnson, Jul 09 2010

a(26) > 5*10^12. - Giovanni Resta, Apr 25 2017

Crossrefs

Cf. A088821-A088824.

Programs

Mathematica

gp[n_] := If[n==1, 0, FactorInteger[n][[-1, 1]]]; Flatten@ Position[ Accumulate[ gp /@ Range[10^5]] / Range[10^5], Integer] (* _Giovanni Resta, Apr 25 2017 *)

Formula

Solutions to Mod[A088822[x], x]=0.

Extensions

More terms from Ray Chandler, Oct 31 2003

a(17)-a(20) from Donovan Johnson, Nov 01 2009

a(21) from Donovan Johnson, Jul 09 2010

a(22)-a(25) from Giovanni Resta, Apr 25 2017