A330289 Numbers all of whose divisors are odious numbers (A000069) with a record number of divisors.

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).

Links

Amiram Eldar, Table of n, a(n) for n = 1..43

Amiram Eldar, Table of n, a(n), A000005(a(n)) for n = 1..43

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

Adjacent sequences: A330286 A330287 A330288 * A330290 A330291 A330292

Keyword

nonn,base

Author

Amiram Eldar, Dec 09 2019

Status

approved