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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
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<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; a:=[]; niven:=func<n|n mod &+Intseq(n) eq 0>; [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
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.)