A334531 Numbers that are both binary Niven numbers and binary Smith numbers.

55, 185, 205, 222, 246, 438, 623, 822, 973, 1503, 1939, 2359, 2471, 3126, 3205, 3462, 3573, 3661, 3771, 3846, 4711, 5877, 5949, 6093, 6198, 6655, 6918, 7083, 7550, 7931, 8151, 8170, 9567, 9863, 10265, 10683, 11241, 12280, 12318, 12486, 12678, 13695, 13790, 13820

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

Intersection of A049445 and A278909.

Cf. A334527.

Sequence in context: A039781 A135657 A178793 * A161763 A189005 A105442

Adjacent sequences: A334528 A334529 A334530 * A334532 A334533 A334534

Keyword

nonn,base

Author

Amiram Eldar, May 05 2020

Status

approved