A111360 Integers k such that sigma(k) + prime(k) is divisible by k.

1, 2, 3, 9, 21, 129, 5663, 40087, 184971, 246901, 251737, 1610143, 3098384123, 19819945093, 21323898091, 123112069843, 130057547087

Offset: 1

Author

Ray G. Opao, Nov 07 2005

Keywords

• nonn
• more

Comments

a(18) > 10^13, if it exists. - Giovanni Resta, Jan 05 2020

Examples

			The divisors of 21 are 1,3,7,21 and the 21st prime is 73. 1+3+7+21+73 = 105, which is divisible by 21.
		

Crossrefs

Cf. A000203, A038607.

Programs

Mathematica

Select[Range[10^8], Mod[Prime[ # ] + Plus @@ Divisors[ # ], # ] == 0 &] (* Ray Chandler, Jan 24 2006 *)

PARI

p=2; for(n=1,100000000, if( (sigma(n)+p) % n == 0, print(n) ) ; p=nextprime(p+1) ; ) \\ R. J. Mathar, Feb 11 2008

Extensions

a(13)-a(15) from Donovan Johnson, Apr 22 2008

New name from Michel Marcus, Dec 10 2019

a(16)-a(17) from Giovanni Resta, Dec 12 2019