A204830 - OEIS

%I #37 Jun 22 2024 08:16:44

%S 120,180,240,360,420,480,504,540,600,660,672,720,780,840,960,1080,

%T 1260,1320,1440,1512,1560,1584,1620,1680,1800,1848,1890,1920,1980,

%U 2016,2040,2160,2184,2280,2340,2352,2376,2400,2520,2640,2688,2760,2772,2856,2880,2940,3000

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

%C Subsequence of the intersection of A023197 and A087943.

%C If m is a term then so is m*p^k when p is coprime to m. - _David A. Corneth_, Mar 09 2024

%C 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

%C 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

%H David A. Corneth, <a href="/A204830/b204830.txt">Table of n, a(n) for n = 1..10296</a> (first 500 terms from Paolo P. Lava, terms <= 550000).

%H Farid Jokar, <a href="https://arxiv.org/abs/2207.09053">On k-layered numbers</a>, arXiv:2207.09053 [math.NT], 2022.

%e 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).

%Y 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.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Jan 22 2012