OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Wayne L. McDaniel, On the Intersection of the Sets of Base b Smith Numbers and Niven Numbers, Missouri Journal of Mathematical Sciences, Vol. 2, No. 3 (1990), pp. 132-136.
EXAMPLE
The binary representation of 55 is 110111. It is a binary Niven number since 1 + 1 + 0 + 1 + 1 + 1 = 5 is a divisor of 55. It is also a binary Smith number since its prime factorization, 5 * 11, is 101 * 1011 in binary representation, and 1 + 1 + 0 + 1 + 1 + 1 = (1 + 0 + 1) + (1 + 0 + 1 + 1). Thus 55 is a term.
MATHEMATICA
binWt[n_] := DigitCount[n, 2, 1]; binNivenSmithQ[n_] := Divisible[n, (bw = binWt[n])] && CompositeQ[n] && Plus @@ (Last@# * binWt[First@#] & /@ FactorInteger[n]) == bw; Select[Range[10^4], binNivenSmithQ]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, May 05 2020
STATUS
approved