A292413 - OEIS

%I #15 Sep 19 2017 06:48:10

%S 4,3,14,54,1496,42520,177263760,11712677760

%N a(n) is the smallest k such that sigma(sigma(k)) = sigma(sigma(k) - k) + n*k, or 0 if no such k exists.

%C For n <= 5, the values k <= 10^6 such that sigma(sigma(k)) = sigma(sigma(k) - k) + n*k are:

%C For n = 1; 4, 144, 16384.

%C For n = 2; 3, 7, 8, 31, 84, 127, 8191, 35743, 42048, 131071, 524287.

%C For n = 3; 14, 20, 372, 1081, 16246, 98292.

%C For n = 4; 54, 168, 308, 504, 994, 3870, 4994, 7800, 16488, 17360, 51995, 475664.

%C For n = 5; 1496, 1704, 14976, 21552, 379938, 854168.

%C a(10) = 16708685994, a(9) > 6*10^11. - _Giovanni Resta_, Sep 18 2017

%o (PARI) a(n) = {my(k=2); while(sigma(sigma(k))-sigma(sigma(k)-k) != n*k, k++); k; }

%Y Cf. A000203, A051027, A272930, A291881.

%K nonn,more

%O 1,1

%A _Altug Alkan_, Sep 16 2017

%E a(8) from _Giovanni Resta_, Sep 18 2017