A378652 Numbers whose divisors can be partitioned in exactly two ways into two disjoint sets with the same sum.

40, 42, 54, 66, 78, 102, 112, 114, 138, 174, 186, 204, 222, 228, 246, 258, 276, 282, 318, 348, 354, 366, 372, 402, 414, 416, 426, 438, 444, 460, 474, 490, 492, 498, 500, 516, 522, 534, 544, 558, 564, 572, 580, 582, 606, 608, 618, 620, 636, 642, 654, 666, 678, 708, 732, 740, 762, 786, 804, 812, 820, 822, 834, 852

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..15509

Formula

{k such that A083206(k) = 2}.

Example

Divisors of 40 are [1, 2, 4, 5, 8, 10, 20, 40], whose sum is 90. These can be partitioned in two ways so that both the set and its complement has sum 45, either as 40+5 = 1+2+4+8+10+20 or as 40+4+1 = 2+5+8+10+20, therefore 40 is included in this sequence.

Prog

(PARI) is_A378652 = A378651;

Crossrefs

Cf. A083206, A083209, A378651 (characteristic function).

Subsequence of Zumkeller numbers, A083207.

Sequence in context: A128843 A214563 A111167 * A392952 A070980 A131535

Adjacent sequences: A378649 A378650 A378651 * A378653 A378654 A378655

Keyword

nonn

Author

Antti Karttunen, Dec 02 2024

Status

approved