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A371909 Number of divisors of the partial sums of A109890.

%I A371909 #5 Apr 28 2024 11:39:59
%S A371909 1,2,4,6,5,8,9,6,6,12,6,9,16,15,12,14,20,16,18,15,8,12,4,8,8,8,12,16,
%T A371909 12,8,8,12,12,16,16,8,48,8,8,8,16,20,8,16,48,12,4,16,4,12,8,8,18,16,
%U A371909 60,12,20,8,24,24,15,36,40,36,12,8,20,32,8,12,36,16,24
%N A371909 Number of divisors of the partial sums of A109890.
%H A371909 Michael De Vlieger, <a href="/A371909/b371909.txt">Table of n, a(n) for n = 1..10000</a>
%F A371909 a(n) = A000005(A109735(n)).
%t A371909 nn = 120; c[_] := False;
%t A371909 Array[Set[{a[#], c[#]}, {#, True}] &, 2]; s = a[1] + a[2];
%t A371909 {1}~Join~Reap[Do[k = SelectFirst[Divisors[s], ! c[#] &];
%t A371909      c[k] = True; Sow[DivisorSigma[0, s]];
%t A371909      s += k, {n, 3, nn}] ][[-1, 1]]
%Y A371909 Cf. A000005, A109735, A109890, A371910.
%K A371909 nonn
%O A371909 1,2
%A A371909 _Michael De Vlieger_, Apr 26 2024