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A376844
Numbers k such that (k + k')' = k' + k'', where ' denotes the arithmetic derivative A003415.
6
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
1,2
EXAMPLE
a(4) = 98 is a term because 98' = 77, 77' = 18 and (98 + 77)' = 175' = 95 = 77 + 18.
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]);
KEYWORD
nonn
AUTHOR
Robert Israel, Oct 06 2024
STATUS
approved