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

1,1

Comments

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, ...

Links

Table of n, a(n) for n=1..41.

Example

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

Prog

(Magma) [n: n in[2..1000000] | SumOfDivisors(SumOfDivisors(n)- n) mod n eq 0]
(PARI) isok(n) = (n!=1) && !(sigma(sigma(n)-n) % n); \\ Michel Marcus, Mar 25 2018

Crossrefs

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

Sequence in context: A059889 A058011 A278374 * A366557 A089330 A227553

Adjacent sequences: A300655 A300656 A300657 * A300659 A300660 A300661

Keyword

nonn

Author

Jaroslav Krizek, Mar 24 2018

Status

approved