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Integers k such that sigma(k) + prime(k) is divisible by k.
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%I #29 Jan 05 2020 06:00:45

%S 1,2,3,9,21,129,5663,40087,184971,246901,251737,1610143,3098384123,

%T 19819945093,21323898091,123112069843,130057547087

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

%C a(18) > 10^13, if it exists. - _Giovanni Resta_, Jan 05 2020

%e 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.

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

%o (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

%Y Cf. A000203, A038607.

%K nonn,more

%O 1,2

%A _Ray G. Opao_, Nov 07 2005

%E a(13)-a(15) from _Donovan Johnson_, Apr 22 2008

%E New name from _Michel Marcus_, Dec 10 2019

%E a(16)-a(17) from _Giovanni Resta_, Dec 12 2019