A356020 Positions of records in A356018, i.e., integers whose number of evil divisors sets a new record.

1, 3, 6, 12, 18, 30, 60, 90, 120, 180, 360, 540, 720, 1080, 1440, 2160, 3780, 4320, 6120, 7560, 8640, 12240, 15120, 24480, 27720, 30240, 36720, 48960, 50400, 55440, 73440, 83160, 110880, 128520, 138600, 166320, 221760, 257040, 277200, 332640, 471240, 514080, 554400

Offset

1,2

Comments

Corresponding records of number of evil divisors are 0, 1, 2, 3, 4, 6, 9, 10, 12, 15, ...

Links

David A. Corneth, Table of n, a(n) for n = 1..189

Example

60 is in the sequence because A356018(60) = 9 is larger than any earlier value in A356018.

Mathematica

f[n_] := DivisorSum[n, 1 &, EvenQ[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 24 2022 *)

Prog

(PARI) upto(n) = my(res = List(), r=-1); forfactored(i=1, n, if(numdiv(i[2]) > r, d = divisors(i[2]); c=sum(j=1, #d, isevil(d[j])); if(c>r, r=c; listput(res, i[1])))); res
isevil(n) = bitand(hammingweight(n), 1)==0 \\ David A. Corneth, Jul 24 2022
(Python)
from sympy import divisors
from itertools import count, islice
def c(n): return bin(n).count("1")&1 == 0
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(), 40))) # Michael S. Branicky, Jul 24 2022

Crossrefs

Cf. A001969, A093688, A093696, A356018, A356019.

Similar sequences: A093036, A093037, A330815, A350756, A355969.

Sequence in context: A006156 A171370 A061776 * A341316 A298029 A327328

Adjacent sequences: A356017 A356018 A356019 * A356021 A356022 A356023

Keyword

nonn,base

Author

Bernard Schott, Jul 24 2022

Extensions

More terms from Amiram Eldar, Jul 24 2022

Status

approved