A375238 - OEIS

%I #8 Aug 06 2024 21:53:32

%S 5,9,22,35,65,63,70,62,82,110,75,143,130,169,142,186,170,194,230,284,

%T 234,195,147,345,238,245,323,290,286,294,285,334,430,534,458,255,385,

%U 434,390,418,374,399,441,526,518,382,748,598,578,454,455,585,507,435,582

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

%e a(7) = 70 and 70 has 7 partitions of three numbers, x, y and z, for which 70' = x' + y' + z' = 59. In fact:

%e 5' + 21' + 44' = 1 + 10 + 48 = 59;

%e 6' + 14' + 50' = 5 + 9 + 45 = 59;

%e 6' + 22' + 42' = 5 + 13 + 41 = 59;

%e 10' + 10' + 50' = 7 + 7 + 45 = 59;

%e 13' + 24' + 33' = 1 + 44 + 14 = 59;

%e 13' + 27' + 30' = 1 + 27 + 31 = 59;

%e 14' + 14' + 42' = 9 + 9 + 41 = 59.

%e Furthermore 70 is the minimum number to have this property.

%Y Cf. A003415, A212662, A373047, A375154.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Aug 06 2024