The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A204831 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A204831

Numbers n whose divisors can be partitioned into four disjoint sets whose sums are all sigma(n)/4.
(history; published version)

#16 by Michael De Vlieger at Wed Jul 20 11:15:49 EDT 2022

STATUS

proposed

approved

#15 by Michel Marcus at Wed Jul 20 10:58:38 EDT 2022

STATUS

editing

proposed

#14 by Michel Marcus at Wed Jul 20 10:58:35 EDT 2022

LINKS

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

STATUS

approved

editing

#13 by Susanna Cuyler at Sat Jan 12 20:45:10 EST 2019

STATUS

proposed

approved

#12 by Jon E. Schoenfield at Sat Jan 12 20:25:30 EST 2019

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Sat Jan 12 20:25:27 EST 2019

COMMENTS

Subsequence of A023198 (numbers n such that sigma(n) >= 4n).

EXAMPLE

Number 27720 is in the sequence because sigma(27720)/4 = 28080 = 360 + 27720 = 20 + 60 + 280 + 2310 + 4620 + 6930 + 13860 = 9 + 30 + 420 + 1540 + 1980 + 2772 + 3080 + 3465 + 5544 + 9240 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 11 + 12 + 14 + 15 + 18 + 21 + 22 + 24 + 28 + 33 + 35 + 36 + 40 + 42 + 44 + 45 + 55 + 56 + 63 + 66 + 70+ 72 + 77 + 84 + 88 + 90 + 99 + 105 + 110 + 120 + 126 + 132 + 140 + 154 + 165 + 168 + 180 + 198 + 210 + 220 + 231 + 252 + 264+ 308 + 315 + 330 + 385 + 396 + 440 + 462 + 495 + 504 + 616 + 630 + 660 + 693 + 770 + 792 + 840 + 924 + 990 + 1155 + 1260 + 1320 + 1386 + 1848 + 2520 + 3960 (summands are all divisors of 27720).

MAPLE

A204831(100000); # _Paolo P. Lava, _, Jan 24 2012.

CROSSREFS

Cf. A083207 (Zumkeller numbers--numbers n whose divisors can be partitioned into two disjoint sets whose sums are both sigma(n)/2), A204830 (numbers n whose divisors can be partitioned into three disjoint sets whose sums are all sigma(n)/3).

STATUS

approved

editing

#10 by Russ Cox at Fri Mar 30 19:00:28 EDT 2012

AUTHOR

_Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), _, Jan 22 2012

Discussion

Fri Mar 30

19:00

OEIS Server: https://oeis.org/edit/global/299

#9 by Joerg Arndt at Fri Feb 03 12:19:14 EST 2012

STATUS

proposed

approved

#8 by Paolo P. Lava at Fri Feb 03 05:48:47 EST 2012

STATUS

editing

proposed

#7 by Paolo P. Lava at Fri Feb 03 05:48:42 EST 2012

CROSSREFS

Cf. A083207 (Zumkeller numbers-numbers n whose divisors can be partitioned into three two disjoint sets whose sums are both sigma(n)/2), A204830 (numbers n whose divisors can be partitioned into three disjoint sets whose sums are all sigma(n)/3).

STATUS

approved

editing