A364976 3-abundant numbers k such that k/(sigma(k)-3*k) is an integer.

180, 240, 360, 420, 540, 600, 780, 1080, 1344, 1872, 1890, 2016, 2184, 2352, 2376, 2688, 3192, 3276, 3744, 4284, 4320, 4680, 5292, 5376, 5796, 6048, 6552, 7128, 7440, 8190, 10416, 13776, 14850, 18600, 19824, 19872, 20496, 21528, 22932, 25056, 26208, 26496, 26784

Offset: 1

Author

Amiram Eldar, Aug 15 2023

Keywords

• nonn

Comments

Analogous to A153501 as 3-abundant numbers (A068403) are analogous to abundant numbers (A005101).

Numbers k such that the sum of the divisors of k except for one of them is equal to 3*k.

Examples

			180 is a term since sigma(180) - 3*180 = 6 > 0 and 180 is divisible by 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..576 (terms below 2.5*10^10)

Crossrefs

Subsequence of A068403.

A027687 is a subsequence.

Cf. A000203 (sigma), A005101, A005820, A055153, A153501, A160320, A218404, A218406, A329189, A364977.

Programs

Mathematica

Select[Range[27000], (d = DivisorSigma[1, #] - 3*#) > 0 && Divisible[#, d] &]

PARI

is(n) = {my(d = sigma(n) - 3*n); d > 0 && n%d == 0;}