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

1,1

Links

Table of n, a(n) for n=1..55.

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

Cf. A003415, A212662, A373047, A375154.

Sequence in context: A110200 A063404 A102177 * A299266 A219521 A215178

Adjacent sequences: A375235 A375236 A375237 * A375239 A375240 A375241

Keyword

nonn,base,easy

Author

Paolo P. Lava, Aug 06 2024

Status

approved