A204830 Numbers k whose divisors can be partitioned into three disjoint sets whose sums are all sigma(k)/3.

120, 180, 240, 360, 420, 480, 504, 540, 600, 660, 672, 720, 780, 840, 960, 1080, 1260, 1320, 1440, 1512, 1560, 1584, 1620, 1680, 1800, 1848, 1890, 1920, 1980, 2016, 2040, 2160, 2184, 2280, 2340, 2352, 2376, 2400, 2520, 2640, 2688, 2760, 2772, 2856, 2880, 2940, 3000

Offset: 1

Author

Jaroslav Krizek, Jan 22 2012

Keywords

• nonn

Comments

Subsequence of the intersection of A023197 and A087943.

If m is a term then so is m*p^k when p is coprime to m. - David A. Corneth, Mar 09 2024

Is this sequence equal to the sequence: "Numbers k such that sigma(k) is divisible by 3 and sigma(k) >= 3*k"? - David A. Corneth, Mar 17 2024

Answer: No. The numbers k with sigma(k) >= 3k and sigma(k) divisible by 3 that are not in this sequence are in A306476. - Amiram Eldar, Jun 22 2024

Examples

			180 is a term because sigma(180)/3 = 182 = 2 + 180 = 1+3+4+5+6+9+10+15+18+30+36+45 = 12+20+60+90 (summands are all the divisors of 180).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10296 (first 500 terms from Paolo P. Lava, terms <= 550000).
• Farid Jokar, On k-layered numbers, arXiv:2207.09053 [math.NT], 2022.

Crossrefs

Cf. A023197, A083207 (Zumkeller numbers -- numbers k whose divisors can be partitioned into two disjoint sets whose sums are both sigma(k)/2), A087943, A204831 (numbers k whose divisors can be partitioned into four disjoint sets whose sums are all sigma(k)/4), A306476.