A345265 - OEIS

%I #7 Jun 12 2021 17:33:58

%S 1,6,30,36,3130,46914,823550,200,1467,10000100110,285311670622,

%T 5973996,302875106592266,11112006930971730,437893890381622140,1040,

%U 827240261886336764194,68036454,1978419655660313589123998,20480003200820,5842587018385982523182222244,341427877364220141714948135418

%N a(n) = Sum_{d|n} n^rad(d).

%F a(p) = Sum_{d|p} p^rad(d) = p^1 + p^p = p^p + p, for p prime.

%e a(8) = Sum_{d|8} 8^rad(d) = 8^1 + 8^2 + 8^2 + 8^2 = 200.

%t Table[Sum[(1 - Ceiling[n/i] + Floor[n/i]) n^Product[k^((PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[i/k] + Floor[i/k])), {k, i}], {i, n}], {n, 30}]

%o (PARI) rad(n) = factorback(factorint(n)[, 1]);

%o a(n) = sumdiv(n, d, n^rad(d)); \\ _Michel Marcus_, Jun 12 2021

%Y Cf. A007947 (rad), A101340.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 12 2021