A093687 Numbers k such that the total number of 1's in the binary expansion of all the divisors of k sets a new record.

1, 2, 3, 6, 12, 18, 24, 30, 60, 90, 120, 180, 252, 360, 420, 504, 540, 630, 756, 840, 1080, 1260, 1980, 2520, 3780, 5040, 6300, 7560, 12600, 13860, 15120, 21420, 25200, 27720, 32760, 41580, 42840, 49140, 55440, 65520, 81900, 83160, 98280, 128520, 138600

Offset: 1

Author

Jason Earls, May 16 2004

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..120

Crossrefs

Cf. A093653.

Programs

Mathematica

a[n_] := Plus @@ DigitCount[Divisors[n], 2, 1]; am = -1; c = 0; seq={}; Do[a1 = a[n]; If[a1 > am, am = a1; c++; AppendTo[seq, n]], {n, 1, 10^4}]; seq (* Amiram Eldar, Dec 17 2019 *)

Python

# uses imports and definitions in A093653
from itertools import count, islice
def f(n): return A093653(n)
def agen(r=0): yield from ((m, r:=fm)[0] for m in count(1) if (fm:=f(m))>r)
print(list(islice(agen(), 45))) # Michael S. Branicky, Feb 15 2023