A247111 -id:A247111 - cp's OEIS frontend

A300658 Numbers m that divide sigma(sigma(m) - m) where sigma is the sum of divisors function (A000203).

4, 6, 8, 28, 32, 36, 78, 84, 128, 168, 252, 496, 504, 532, 756, 1488, 2808, 3720, 4464, 5928, 8128, 8192, 13392, 24384, 61236, 73152, 78120, 131072, 183708, 217728, 219456, 425880, 458640, 524288, 1084752, 1834560, 2204280, 3254256, 6120432, 6386688, 11007360

Offset: 1

Jaroslav Krizek, Mar 24 2018

nonn

Numbers m that divide A072869(m).
Numbers m such that sigma(sigma(m)-m) = k*m for k = 1 - 5:
k = 1:    4, 8, 32, 128, 8192, 131072, 524288, 2147483648, ... (A072868),
k = 2:    6, 28, 36, 496, 8128, 33550336, 8589869056, ... (A247111),
k = 3:    78, 532, ...,
k = 4:    84, 252, 756, 1488, 4464, 13392, 24384, 61236, 73152, ...,
k = 5:    168, 2808, 5928, 6120432, ...
Perfect numbers (A000396) are terms.
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, ...
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, ...

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

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

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

isok(n) = (n!=1) && !(sigma(sigma(n)-n) % n); \\ Michel Marcus, Mar 25 2018

cp's OEIS Frontend

A300658 Numbers m that divide sigma(sigma(m) - m) where sigma is the sum of divisors function (A000203).

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