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

1,2

Comments

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

Links

Table of n, a(n) for n=1..40.

Example

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

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 *)

Prog

(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

Crossrefs

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

Similar sequences: A093036, A093037, A330815, A340549.

Sequence in context: A318767 A208531 A349052 * A308542 A326116 A054189

Adjacent sequences: A355966 A355967 A355968 * A355970 A355971 A355972

Keyword

nonn,base

Author

Bernard Schott, Jul 22 2022

Extensions

More terms from Amiram Eldar, Jul 22 2022

Status

approved