cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A334531 #11 May 06 2020 01:46:36
%S A334531 55,185,205,222,246,438,623,822,973,1503,1939,2359,2471,3126,3205,
%T A334531 3462,3573,3661,3771,3846,4711,5877,5949,6093,6198,6655,6918,7083,
%U A334531 7550,7931,8151,8170,9567,9863,10265,10683,11241,12280,12318,12486,12678,13695,13790,13820
%N A334531 Numbers that are both binary Niven numbers and binary Smith numbers.
%H A334531 Amiram Eldar, <a href="/A334531/b334531.txt">Table of n, a(n) for n = 1..10000</a>
%H A334531 Wayne L. McDaniel, <a href="https://doi.org/10.35834/1990/0203132">On the Intersection of the Sets of Base b Smith Numbers and Niven Numbers</a>, Missouri Journal of Mathematical Sciences, Vol. 2, No. 3 (1990), pp. 132-136.
%e A334531 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.
%t A334531 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]
%Y A334531 Intersection of A049445 and A278909.
%Y A334531 Cf. A334527.
%K A334531 nonn,base
%O A334531 1,1
%A A334531 _Amiram Eldar_, May 05 2020