A364977 Numbers k such that k/(3*k - sigma(k)) is a positive integer.

6, 24, 28, 60, 84, 168, 252, 270, 336, 496, 630, 756, 792, 864, 924, 936, 1140, 1170, 1488, 1638, 2268, 2808, 2970, 3672, 4464, 5148, 5472, 6804, 7308, 7644, 8128, 8700, 8910, 9300, 9936, 11172, 13392, 16368, 18018, 20196, 20412, 22230, 24384, 25116, 27888, 31968

Offset: 1

Author

Amiram Eldar, Aug 15 2023

Keywords

• nonn

Comments

Analogous to A271816 as 3-abundant numbers (A068403) are analogous to abundant numbers (A005101).

Numbers k such that the sum of the divisors of k with one of them added twice is equal to 3*k.

The perfect numbers (A000396) are all terms.

For all the terms k, 2 <= sigma(k)/k < 3, i.e., they are all nondeficient numbers (A023196), and none are 3-abundant (A068403).

Examples

			6 is a term since 3*6 - sigma(6) = 6 > 0 and 6 is divisible by 6.
24 is a term since 3*24 - sigma(24) = 12 > 0 and 24 is divisible by 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..600

Crossrefs

Cf. A000203 (sigma), A000396, A023196, A068403, A271816, A329189, A364976.

Programs

Mathematica

Select[Range[32000], (d = 3*# - DivisorSigma[1, #]) > 0 && Divisible[#, d] &]

PARI

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