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

Author

Bernard Schott, Jul 24 2022

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

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

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

Programs

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 *)

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

Extensions

More terms from Amiram Eldar, Jul 24 2022