A355969 Positions of records in A227872, i.e., integers whose number of odious divisors sets a new record.

1, 2, 4, 8, 16, 28, 56, 84, 112, 168, 336, 672, 1344, 2184, 4368, 8736, 17472, 30576, 34944, 41664, 48048, 61152, 80080, 83328, 96096, 122304, 160160, 192192, 240240, 320320, 336336, 480480, 672672, 960960, 1345344, 1681680, 1921920, 2489760, 2690688, 2738736

Offset: 1

Author

Bernard Schott, Jul 22 2022

Keywords

• nonn
• base

Comments

Corresponding records of number of odious divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, ...

Examples

			a(7) = 56 is in the sequence because A227872(56) = 8 is larger than any earlier value in A227872.
		

Crossrefs

Cf. A000069, A093696, A227872, A330289, A355968.

Similar sequences: A093036, A093037, A330815, A340549.

Programs

Mathematica

f[n_] := DivisorSum[n, 1 &, OddQ[DigitCount[#, 2, 1]] &]; fm = -1; s = {}; Do[If[(fn = f[n]) > fm, fm = fn; AppendTo[s, n]], {n, 1, 10^5}]; s (* Amiram Eldar, Jul 22 2022 *)

PARI

lista(nn)= my(list = List(), m=0, new); for (n=1, nn, new = sumdiv(n, d, isod(d)); if (new > m, listput(list, n); m = new);); Vec(list); \\ Michel Marcus, Jul 22 2022

Python

from sympy import divisors
from itertools import count, islice
def c(n): return bin(n).count("1")&1
def f(n): return sum(1 for d in divisors(n, generator=True) if c(d))
def agen(record=-1):
    for k in count(1):
        if f(k) > record: record = f(k); yield k
print(list(islice(agen(), 30))) # Michael S. Branicky, Jul 23 2022

Extensions

More terms from Amiram Eldar, Jul 22 2022