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a(n) = Sum_{k=1..n} k^Omega(k).
2

%I #13 Jun 25 2022 00:25:59

%S 1,3,6,22,27,63,70,582,663,763,774,2502,2515,2711,2936,68472,68489,

%T 74321,74340,82340,82781,83265,83288,415064,415689,416365,436048,

%U 458000,458029,485029,485060,34039492,34040581,34041737,34042962,35722578,35722615,35724059,35725580,38285580

%N a(n) = Sum_{k=1..n} k^Omega(k).

%H Michael De Vlieger, <a href="/A347616/b347616.txt">Table of n, a(n) for n = 1..1000</a>

%e a(5) = Sum_{k=1..5} k^Omega(k) = 1^0 + 2^1 + 3^1 + 4^2 + 5^1 = 27.

%t Table[Sum[k^PrimeOmega[k], {k, n}], {n, 40}]

%o (PARI) a(n) = sum(k=1, n, k^bigomega(k)); \\ _Michel Marcus_, Sep 09 2021

%Y Cf. A001222 (Omega), A347614.

%Y Partial sums of A176029.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Sep 08 2021