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Jacobsthal-Niven numbers: numbers that are divisible by the sum of the digits in their Jacobsthal representation (A280049).
7

%I #6 Jul 15 2023 05:53:05

%S 1,2,3,4,6,8,9,11,12,14,15,16,20,22,24,27,28,32,33,36,40,42,43,44,45,

%T 46,48,51,52,54,56,57,60,68,72,75,76,84,86,87,88,92,93,95,96,99,100,

%U 104,105,108,112,115,117,120,125,126,128,129,132,135,136,138,140

%N Jacobsthal-Niven numbers: numbers that are divisible by the sum of the digits in their Jacobsthal representation (A280049).

%C Numbers k such that A364215(k) | k.

%C A007583 is a subsequence since A364215(A007583(n)) = 1 for n >= 0.

%H Amiram Eldar, <a href="/A364216/b364216.txt">Table of n, a(n) for n = 1..10000</a>

%t seq[kmax_] := Module[{m = 1, s = {}}, Do[If[Divisible[k, DigitCount[m, 2, 1]], AppendTo[s, k]]; While[m++; OddQ[IntegerExponent[m, 2]]], {k, 1, kmax}]; s]; seq[140]

%o (PARI) lista(kmax) = {my(m = 1); for(k = 1, kmax, if( !(k % sumdigits(m, 2)), print1(k,", ")); until(valuation(m, 2)%2 == 0, m++));}

%Y Cf. A280049, A364215.

%Y Subsequences: A007583, A364217, A364218, A364219, A364220, A364221.

%Y Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351714, A351719, A352089, A352107, A352320, A352342, A352508.

%K nonn,base,easy

%O 1,2

%A _Amiram Eldar_, Jul 14 2023