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

Author

Antti Karttunen, Dec 02 2024

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Subsequence of Zumkeller numbers, A083207.

Programs

PARI

is_A378652 = A378651;

Formula

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