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 A349484 Niven numbers whose arithmetic derivative is also a Niven number (A005349). 1
 2, 3, 4, 5, 6, 7, 8, 9, 10, 18, 20, 21, 27, 36, 48, 50, 54, 72, 81, 100, 108, 111, 112, 135, 153, 156, 180, 192, 201, 209, 210, 216, 224, 225, 230, 243, 280, 288, 306, 324, 336, 351, 364, 378, 392, 400, 405, 407, 420, 432, 441, 480, 481, 486, 500, 504, 511, 512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is infinite because the numbers of the form m = 2*10^(10^k), k >= 1, are terms. Indeed, m is a Niven number, m' = 10^(10^k) + 2*10^k*10^(10^k - 1)*7 = 10^(10^k - 1)*(10 + 140*10^k) = 10^(10^k)*(1 + 14*10^k), digsum(m') = 6 and m' is divisible by 6, so it is a Niven number. LINKS Table of n, a(n) for n=1..58. EXAMPLE 2 = A005349(2) and 2' = 1 = A005349(1), so 2 is a term. 18 = A005349(12) and 18' = 21 = A005349(14), so 18 is a term. MATHEMATICA nivenQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[2, 512], And @@ nivenQ /@ {#, d[#]} &] (* Amiram Eldar, Nov 20 2021 *) PROG (Magma) f:=func; a:=[]; niven:=func; [n:n in [2..520]|niven(n) and niven(Floor(f(n)))]; CROSSREFS Cf. A002808, A005349 (Niven numbers), A003415 (arithmetic derivative). Sequence in context: A032345 A023765 A032906 * A075905 A321767 A207506 Adjacent sequences: A349481 A349482 A349483 * A349485 A349486 A349487 KEYWORD nonn,base AUTHOR Marius A. Burtea, Nov 20 2021 STATUS approved

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Last modified July 20 20:25 EDT 2024. Contains 374459 sequences. (Running on oeis4.)