%I #32 Jan 26 2022 02:30:58
%S 1,3,4,6,9,27,34,68,94,235,289,578,799,1921,9683,16021,27421,54842,
%T 69301,138602,434789,1787371,5179771,5655149,9653251,10209853,
%U 20419706,43184409,301039141,611363527,1274384647,5084853899,14906805553,14946637163,22591381313,69291164983
%N Records in A095258.
%H Michael De Vlieger, <a href="/A350741/b350741.txt">Table of n, a(n) for n = 1..161</a>
%t c[_] = 0; j = c[1] = r = 1; s = 3; Prepend[Reap[Do[d = Divisors[s]; k = 1; While[c[d[[k]]] > 0, k++]; Set[k, d[[k]]]; Set[c[k], i]; If[k > r, r = k; Sow[r]]; j = k; s += k, {i, 2, 2100}] ][[-1, -1]], 1]
%o (Python)
%o from itertools import islice
%o from sympy import divisors
%o def A350741_gen(): # generator of terms
%o bset, c, s = {1}, 1, 3
%o yield 1
%o while True:
%o for d in divisors(s):
%o if d not in bset:
%o if d > c:
%o yield d
%o c = d
%o bset.add(d)
%o s += d
%o break
%o A350741_list = list(islice(A350741_gen(),20)) # _Chai Wah Wu_, Jan 25 2022
%Y Cf. A095258.
%K nonn
%O 1,2
%A _Michael De Vlieger_, Jan 23 2022