A337741 Numbers all of whose divisors are Niven numbers (A005349).

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.

Links

Table of n, a(n) for n=1..31.

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.

Cf. A332268, A335708, A335709.

Similar sequences: A062687, A190217, A329419.

Sequence in context: A085133 A308560 A285815 * A110806 A357769 A180468

Adjacent sequences: A337738 A337739 A337740 * A337742 A337743 A337744

Keyword

nonn,base,fini,full

Author

Amiram Eldar, Sep 17 2020

Status

approved