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 A344578 a(n) = Sum_{d|n} d * sopf(d). 1

%I

%S 0,4,9,12,25,43,49,28,36,99,121,111,169,179,154,60,289,160,361,247,

%T 268,411,529,247,150,563,117,439,841,558,961,124,592,939,494,408,1369,

%U 1163,802,543,1681,932,1849,991,541,1683,2209,519,392,574,1318,1351,2809,511,1026,959,1624

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

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

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

%t 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}]

%Y Cf. A008472 (sopf).

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, May 23 2021

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Last modified January 25 13:05 EST 2022. Contains 350572 sequences. (Running on oeis4.)