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%I #15 Dec 11 2019 05:05:27
%S 1,2,4,8,16,28,56,112,224,448,728,1456,2912,5824,10192,11648,20384,
%T 27664,40768,55328,110656,221312,442624,885248,1263808,1770496,
%U 2527616,5055232,8077888,10110464,16155776,20220928,32311552,64623104,129246208,258492416,516984832
%N Numbers all of whose divisors are odious numbers (A000069) with a record number of divisors.
%C A number m is in this sequence if it is in A093696, and d(m) > d(k) for all terms k < m in A093696, where d(m) is the number of divisors of m (A000005).
%C The corresponding record numbers of divisors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 20, ... (see the link for more values).
%H Amiram Eldar, <a href="/A330289/b330289.txt">Table of n, a(n) for n = 1..43</a>
%H Amiram Eldar, <a href="/A330289/a330289.txt">Table of n, a(n), A000005(a(n)) for n = 1..43</a>
%e The first 5 terms of A093696 are 1, 2, 4, 7, 8 and their numbers of divisors are 1, 2, 3, 2, 4. The record values 1, 2, 3, and 4 are reached at 1, 2, 4 and 8 that are the first 4 terms of this sequence.
%t odiousQ[n_] := OddQ @ DigitCount[n, 2][[1]]; allDivOdiousQ[n_] := AllTrue[ Divisors[n], odiousQ]; divNumMax = 0; seq={}; Do[If[allDivOdiousQ[n] && (divNum = DivisorSigma[0, n]) > divNumMax, divNumMax = divNum; AppendTo[seq, n]], {n, 1, 3000}]; seq
%Y Subsequence of A000069 and A093696.
%Y Cf. A000005.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Dec 09 2019
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