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%I #13 Nov 12 2023 13:28:27
%S 1,2,1,2,1,3,1,3,2,2,1,5,1,2,2,3,1,4,1,4,2,2,1,6,1,2,2,3,1,5,1,3,2,2,
%T 1,6,1,2,2,5,1,5,1,3,3,2,1,6,1,3,2,3,1,4,1,5,2,2,1,8,1,2,2,3,1,4,1,3,
%U 2,4,1,8,1,2,3,3,1,4,1,6,2,2,1,7,1,2,2,4,1,7
%N Number of divisors of n less than or equal to d(n).
%C First differs from A126131 at a(25) = 1.
%F a(n) = Sum_{d|n, d <= d(n)} 1.
%F a(n) = 1 + Sum_{d|n} (Sum_{i=2..d(n)} ( sign(floor(i/d)) - sign(floor((i-1)/d)) )), where d(n) is the number of divisors of n (A000005).
%e a(8) = 3; There are 3 divisors of 8 that are <= d(8) = 4. They are: {1,2,4}.
%e a(25) = 1; 1 is the only divisor of 25 that is <= d(25) = 3.
%t Table[1 + Sum[Sum[(Sign[Floor[i/k]] - Sign[Floor[(i - 1)/k]]), {i, 2, DivisorSigma[0, n]}] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
%o (PARI) a(n) = my(nd=numdiv(n)); sumdiv(n, d, d <= nd); \\ _Michel Marcus_, Oct 30 2023
%Y Cf. A000005, A126131.
%K nonn,easy
%O 1,2
%A _Wesley Ivan Hurt_, Oct 30 2023
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