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A375238
Least k with exactly n partitions k = x + y + z satisfying k' = x' + y' + z', where k' is the arithmetic derivative of k.
0
5, 9, 22, 35, 65, 63, 70, 62, 82, 110, 75, 143, 130, 169, 142, 186, 170, 194, 230, 284, 234, 195, 147, 345, 238, 245, 323, 290, 286, 294, 285, 334, 430, 534, 458, 255, 385, 434, 390, 418, 374, 399, 441, 526, 518, 382, 748, 598, 578, 454, 455, 585, 507, 435, 582
OFFSET
1,1
EXAMPLE
a(7) = 70 and 70 has 7 partitions of three numbers, x, y and z, for which 70' = x' + y' + z' = 59. In fact:
5' + 21' + 44' = 1 + 10 + 48 = 59;
6' + 14' + 50' = 5 + 9 + 45 = 59;
6' + 22' + 42' = 5 + 13 + 41 = 59;
10' + 10' + 50' = 7 + 7 + 45 = 59;
13' + 24' + 33' = 1 + 44 + 14 = 59;
13' + 27' + 30' = 1 + 27 + 31 = 59;
14' + 14' + 42' = 9 + 9 + 41 = 59.
Furthermore 70 is the minimum number to have this property.
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Paolo P. Lava, Aug 06 2024
STATUS
approved