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A330289
Numbers all of whose divisors are odious numbers (A000069) with a record number of divisors.
7
1, 2, 4, 8, 16, 28, 56, 112, 224, 448, 728, 1456, 2912, 5824, 10192, 11648, 20384, 27664, 40768, 55328, 110656, 221312, 442624, 885248, 1263808, 1770496, 2527616, 5055232, 8077888, 10110464, 16155776, 20220928, 32311552, 64623104, 129246208, 258492416, 516984832
OFFSET
1,2
COMMENTS
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).
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).
EXAMPLE
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.
MATHEMATICA
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
CROSSREFS
Subsequence of A000069 and A093696.
Cf. A000005.
Sequence in context: A127195 A255937 A357763 * A348413 A355968 A177269
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Dec 09 2019
STATUS
approved