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A355969 Positions of records in A227872, i.e., integers whose number of odious divisors sets a new record.

%I A355969 #21 Jul 24 2022 03:57:08
%S A355969 1,2,4,8,16,28,56,84,112,168,336,672,1344,2184,4368,8736,17472,30576,
%T A355969 34944,41664,48048,61152,80080,83328,96096,122304,160160,192192,
%U A355969 240240,320320,336336,480480,672672,960960,1345344,1681680,1921920,2489760,2690688,2738736
%N A355969 Positions of records in A227872, i.e., integers whose number of odious divisors sets a new record.
%C A355969 Corresponding records of number of odious divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, ...
%e A355969 a(7) = 56 is in the sequence because A227872(56) = 8 is larger than any earlier value in A227872.
%t A355969 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 *)
%o A355969 (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
%o A355969 (Python)
%o A355969 from sympy import divisors
%o A355969 from itertools import count, islice
%o A355969 def c(n): return bin(n).count("1")&1
%o A355969 def f(n): return sum(1 for d in divisors(n, generator=True) if c(d))
%o A355969 def agen(record=-1):
%o A355969     for k in count(1):
%o A355969         if f(k) > record: record = f(k); yield k
%o A355969 print(list(islice(agen(), 30))) # _Michael S. Branicky_, Jul 23 2022
%Y A355969 Cf. A000069, A093696, A227872, A330289, A355968.
%Y A355969 Similar sequences: A093036, A093037, A330815, A340549.
%K A355969 nonn,base
%O A355969 1,2
%A A355969 _Bernard Schott_, Jul 22 2022
%E A355969 More terms from _Amiram Eldar_, Jul 22 2022