A376844 Numbers k such that (k + k')' = k' + k'', where ' denotes the arithmetic derivative A003415.

1, 2, 16, 98, 108, 275, 598, 729, 2419, 3503, 5324, 11304, 12500, 35937, 50498, 51179, 58339, 76302, 84375, 107830, 141775, 209663, 324480, 588800, 618434, 1090123, 1532188, 2190240, 2615251, 3175699, 3294172, 3974400, 4159375, 6795761, 8403500, 8831250, 9765625, 10342269, 14784120, 15714364, 16056320

Offset: 1

Author

Robert Israel, Oct 06 2024

Keywords

• nonn

Examples

			a(4) = 98 is a term because 98' = 77, 77' = 18 and (98  + 77)' = 175' = 95 = 77 + 18.
		

Crossrefs

Cf. A003415, A376830, A376831, A376843, A376848, A376849, A376851.

Programs

Maple

deriv:= proc(n) local t; add(n*t[2]/t[1], t = ifactors(n)[2]) end proc:
filter:= proc(n) local s; s:= deriv(n); deriv(n+s) = s + deriv(s) end proc:
select(filter, [$1..10^6]);