

A168012


a(n) = sum of all divisors of all numbers k such that n^2 <= k < (n+1)^2.


4



8, 48, 133, 302, 516, 923, 1346, 2038, 2768, 3891, 4810, 6572, 7959, 10066, 12186, 14944, 17261, 21210, 23992, 28497, 32550, 37742, 42111, 48906, 54252, 61280, 68153, 76958, 82942, 94661, 101882, 113082, 123794, 135583, 145630, 161526
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OFFSET

1,1


LINKS



EXAMPLE

a(2) = 48 because the numbers k are 4,5,6,7 and 8 (since 2^2 <= k < 3^2) and sigma(4) + sigma(5) + sigma(6) + sigma(7) + sigma(8) = 7 + 6 + 12 + 8 + 15 = 48, where sigma(n) is the sum of divisors of n (see A000203).


MATHEMATICA

A168012[n_]:=Sum[DivisorSigma[1, k], {k, n^2, (n+1)^21}];


PROG

(Python)
a, b = n*(n+2), (n1)*(n+1)
return (sum((q:=a//k)*((s:=k<<1)+q+1)(r:=b//k)*(s+r+1) for k in range(1, n))>>1)+5*n+3 # Chai Wah Wu, Oct 23 2023


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



