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A337741
Numbers all of whose divisors are Niven numbers (A005349).
6
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, 243, 324, 486, 648, 972, 1944
OFFSET
1,2
COMMENTS
Since the only prime Niven numbers are the single-digit primes 2, 3, 5 and 7, all the terms are 7-smooth numbers (A002473).
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.
EXAMPLE
6 is a term since all the divisors of 6, i.e., 1, 2, 3 and 6, are Niven numbers.
MATHEMATICA
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
CROSSREFS
Subsequence of A002473 and A005349.
Similar sequences: A062687, A190217, A329419.
Sequence in context: A085133 A308560 A285815 * A110806 A357769 A180468
KEYWORD
nonn,base,fini,full
AUTHOR
Amiram Eldar, Sep 17 2020
STATUS
approved