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A355969
Positions of records in A227872, i.e., integers whose number of odious divisors sets a new record.
6
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, ...
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
Similar sequences: A093036, A093037, A330815, A340549.
Sequence in context: A318767 A208531 A349052 * A308542 A326116 A054189
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jul 22 2022
EXTENSIONS
More terms from Amiram Eldar, Jul 22 2022
STATUS
approved