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a(n) = Sum_{p|n} p^pi(p).
1

%I #9 Jun 13 2021 15:26:23

%S 0,2,9,2,125,11,2401,2,9,127,161051,11,4826809,2403,134,2,410338673,

%T 11,16983563041,127,2410,161053,1801152661463,11,125,4826811,9,2403,

%U 420707233300201,136,25408476896404831,2,161060,410338675,2526,11,6582952005840035281,16983563043

%N a(n) = Sum_{p|n} p^pi(p).

%F a(p) = p^pi(p) for p prime.

%e a(10) = Sum_{p|10} p^pi(p) = 2^1 + 5^3 = 127.

%t Table[Sum[k^PrimePi[k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]

%o (Python)

%o from sympy import primefactors, primepi

%o def A345299(n): return sum(p**primepi(p) for p in primefactors(n)) # _Chai Wah Wu_, Jun 13 2021

%Y Cf. A000720, A066328.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 13 2021