A375238 Least k with exactly n partitions k = x + y + z satisfying k' = x' + y' + z', where k' is the arithmetic derivative of k.

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

Author

Paolo P. Lava, Aug 06 2024

Keywords

• nonn
• base
• easy

Examples

			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

Cf. A003415, A212662, A373047, A375154.