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A300658
Numbers m that divide sigma(sigma(m) - m) where sigma is the sum of divisors function (A000203).
0
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, ...
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 24 2018
STATUS
approved