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%I A337741 #7 Sep 17 2020 20:30:53
%S A337741 1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,36,40,54,63,72,81,108,162,216,
%T A337741 243,324,486,648,972,1944
%N A337741 Numbers all of whose divisors are Niven numbers (A005349).
%C A337741 Since the only prime Niven numbers are the single-digit primes 2, 3, 5 and 7, all the terms are 7-smooth numbers (A002473).
%C A337741 If k is a term, all the divisors of k are also terms. Since all the terms are 7-smooth, every term is of the form p * k, where p is in {2, 3, 5, 7} and k is a smaller term. Thus it is easy to verify that there are only 31 terms in this sequence, and 1944 being the last term.
%e A337741 6 is a term since all the divisors of 6, i.e., 1, 2, 3 and 6, are Niven numbers.
%t A337741 nivenQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; allQ[n_] := AllTrue[Divisors[n], nivenQ]; p = {1, 2, 3, 5, 7}; s = {1}; n = 0; While[Length[s] != n, n = Length[s]; s = Select[Union @ Flatten @ Outer[Times, s, p], allQ]]; s
%Y A337741 Subsequence of A002473 and A005349.
%Y A337741 Cf. A332268, A335708, A335709.
%Y A337741 Similar sequences: A062687, A190217, A329419.
%K A337741 nonn,base,fini,full
%O A337741 1,2
%A A337741 _Amiram Eldar_, Sep 17 2020

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