A300658 - OEIS

%I #19 Sep 08 2022 08:46:20

%S 4,6,8,28,32,36,78,84,128,168,252,496,504,532,756,1488,2808,3720,4464,

%T 5928,8128,8192,13392,24384,61236,73152,78120,131072,183708,217728,

%U 219456,425880,458640,524288,1084752,1834560,2204280,3254256,6120432,6386688,11007360

%N Numbers m that divide sigma(sigma(m) - m) where sigma is the sum of divisors function (A000203).

%C Numbers m that divide A072869(m).

%C Numbers m such that sigma(sigma(m)-m) = k*m for k = 1 - 5:

%C k = 1:    4, 8, 32, 128, 8192, 131072, 524288, 2147483648, ... (A072868),

%C k = 2:    6, 28, 36, 496, 8128, 33550336, 8589869056, ... (A247111),

%C k = 3:    78, 532, ...,

%C k = 4:    84, 252, 756, 1488, 4464, 13392, 24384, 61236, 73152, ...,

%C k = 5:    168, 2808, 5928, 6120432, ...

%C Perfect numbers (A000396) are terms.

%C Corresponding values of (sigma(sigma(m) - m)) / m for numbers m from this sequence: 1, 2, 1, 2, 1, 2, 3, 4, 1, 5, 4, 2, 6, 3, 4, 4, 5, 7, 4, 5, 2, 1, 4, 4, 4, 4, 10, 1, 4, 8, 4, 12, 10, 1, 4, 11, 9, ...

%C Sequence of the smallest numbers k such that sigma(sigma(k) - k) = n*k for n >= 1: 4, 6, 78, 84, 168, 504, 3720, 217728, 2204280, 78120, 1834560, 425880, ...

%e 6 is a term because sigma(sigma(6) - 6) / 6 = 12 / 6 = 2 (integer).

%o (Magma) [n: n in[2..1000000] | SumOfDivisors(SumOfDivisors(n)- n) mod n eq 0]

%o (PARI) isok(n) = (n!=1) && !(sigma(sigma(n)-n) % n); \\ _Michel Marcus_, Mar 25 2018

%Y Cf. A000203, A000396, A072868, A072869, A247111.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Mar 24 2018