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

Author

Amiram Eldar, Dec 09 2019

Keywords

• nonn
• base

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).

Examples

			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.
		

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

Crossrefs

Subsequence of A000069 and A093696.

Cf. A000005.

Programs

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