cp's OEIS Frontend

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

%I A356020 #24 Jul 26 2022 17:47:48
%S A356020 1,3,6,12,18,30,60,90,120,180,360,540,720,1080,1440,2160,3780,4320,
%T A356020 6120,7560,8640,12240,15120,24480,27720,30240,36720,48960,50400,55440,
%U A356020 73440,83160,110880,128520,138600,166320,221760,257040,277200,332640,471240,514080,554400
%N A356020 Positions of records in A356018, i.e., integers whose number of evil divisors sets a new record.
%C A356020 Corresponding records of number of evil divisors are 0, 1, 2, 3, 4, 6, 9, 10, 12, 15, ...
%H A356020 David A. Corneth, <a href="/A356020/b356020.txt">Table of n, a(n) for n = 1..189</a>
%e A356020 60 is in the sequence because A356018(60) = 9 is larger than any earlier value in A356018.
%t A356020 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 *)
%o A356020 (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
%o A356020 isevil(n) = bitand(hammingweight(n), 1)==0 \\ _David A. Corneth_, Jul 24 2022
%o A356020 (Python)
%o A356020 from sympy import divisors
%o A356020 from itertools import count, islice
%o A356020 def c(n): return bin(n).count("1")&1 == 0
%o A356020 def f(n): return sum(1 for d in divisors(n, generator=True) if c(d))
%o A356020 def agen(record=-1):
%o A356020     for k in count(1):
%o A356020         if f(k) > record: record = f(k); yield k
%o A356020 print(list(islice(agen(), 40))) # _Michael S. Branicky_, Jul 24 2022
%Y A356020 Cf. A001969, A093688, A093696, A356018, A356019.
%Y A356020 Similar sequences: A093036, A093037, A330815, A350756, A355969.
%K A356020 nonn,base
%O A356020 1,2
%A A356020 _Bernard Schott_, Jul 24 2022
%E A356020 More terms from _Amiram Eldar_, Jul 24 2022