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A373047
Least k with exactly n partitions k = x + y + z satisfying sigma*(k) = sigma*(x) + sigma*(y) + sigma*(z), where sigma*(k) is the sum of the anti-divisors of k.
2
11, 33, 16, 20, 26, 37, 40, 19, 43, 46, 93, 91, 80, 76, 39, 78, 155, 103, 74, 135, 128, 152, 116, 117, 190, 104, 187, 138, 168, 147, 160, 223, 208, 403, 281, 173, 163, 170, 250, 243, 272, 257, 258, 232, 222, 278, 266, 245, 352, 253, 279, 256, 288, 295, 231, 291
OFFSET
1,1
EXAMPLE
a(7) = 40 and 40 has 7 partitions of three numbers, x, y and
z, for which sigma*(65) = sigma*(x) + sigma*(y) + sigma*(z) = 55. In fact:
sigma*(1) + sigma*+(4) + sigma*(35) = 0 + 3 + 52 = 55;
sigma*(1) + sigma*(12) + sigma*(27) = 0 + 13 + 42 = 55;
sigma*(1) + sigma*(14) + sigma*(25) = 0 + 16 + 39 = 55;
sigma*(4) + sigma*(14) + sigma*(22) = 3 + 16 + 36 = 55;
sigma*(5) + sigma*(8) + sigma*(27) = 5 + 8 + 42 = 55;
sigma*(9) + sigma*(13) + sigma*(18) = 8 + 19 + 28 = 55;
sigma*(10) + sigma*(12) + sigma*(18) = 14 + 13 + 28 = 55;
Furthermore 40 is the minimum number to have this property.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Aug 02 2024
STATUS
approved