A344578 - OEIS

A344578

a(n) = Sum_{d|n} d * sopf(d).

0, 4, 9, 12, 25, 43, 49, 28, 36, 99, 121, 111, 169, 179, 154, 60, 289, 160, 361, 247, 268, 411, 529, 247, 150, 563, 117, 439, 841, 558, 961, 124, 592, 939, 494, 408, 1369, 1163, 802, 543, 1681, 932, 1849, 991, 541, 1683, 2209, 519, 392, 574, 1318, 1351, 2809, 511, 1026, 959, 1624

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OFFSET

1,2

COMMENTS

If p is prime, a(p) = Sum_{d|p} d * sopf(d) = p * p = p^2.

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

a(10) = Sum_{d|10} d * sopf(d) = 1*0 + 2*2 + 5*5 + 10*7 = 99.

MATHEMATICA

Table[Sum[i*Sum[k (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[i/k] + Floor[i/k]), {k, i}] (1 - Ceiling[n/i] + Floor[n/i]), {i, n}], {n, 100}]

CROSSREFS