A326608 Numbers m such that m | A000385(m-1) = Sum_{k=1..m-1} sigma(k) * sigma(m-k).

1, 3, 40, 84, 124, 318, 496, 672, 732, 790, 1320, 1488, 3154, 4464, 5271, 8128, 9156, 9888, 10880, 13392, 14760, 16392, 17019, 22366, 24384, 39424, 57240, 67488, 68237, 73276, 93825, 95728, 106428, 115330, 128982, 138176, 143256, 143780, 144210, 154432, 156360

Offset

1,2

Comments

1 is in the sequence assuming A000385(0) = 0.

The corresponding quotients are 0, 2, 723, 3376, 7196, 48834, 116655, 222646, 263221, 294168, 865608, ...

Includes all the even perfect numbers except for 6 and 28.

The only prime number in the sequence is 3. This follows from formula for A000385 given by Robert Israel. - Luis H. Gallardo, Jun 17 2020

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

Example

3 is in the sequence since 3 is a divisor for A000385(3-1) = 6.

Mathematica

aQ[n_] := Divisible[5 * DivisorSigma[3, n] - (6n - 1) * DivisorSigma[1, n], 12n]; Select[Range[2*10^5], aQ]

Crossrefs

Cf. A000203, A000385, A000396.

Sequence in context: A101014 A262036 A041347 * A160659 A197247 A065815

Adjacent sequences: A326605 A326606 A326607 * A326609 A326610 A326611

Keyword

nonn

Author

Amiram Eldar, Oct 18 2019

Status

approved