A350996 -id:A350996 - cp's OEIS frontend

A350997 a(n) = Sum_{k=1..n} k^rad(k).

1, 5, 32, 48, 3173, 49829, 873372, 873436, 874165, 10000874165, 295312544776, 295315530760, 303170422123013, 11415177247681029, 449309067628540404, 449309067628540660, 827689570953965304837, 827689570953999317061, 1979247345231267588441040

Offset: 1

Wesley Ivan Hurt, Jan 28 2022

nonn

			a(4) = 48; a(4) = Sum_{k=1..4} k^rad(k) = 1^rad(1) + 2^rad(2) + 3^rad(3) + 4^rad(4) = 1^1 + 2^2 + 3^3 + 4^2 = 48.

Wikipedia, Radical of an integer.

Cf. A007947 (rad), A176031, A350996.

f[n_] := n^Times @@ FactorInteger[n][[;; , 1]]; Accumulate @ Array[f, 20] (* Amiram Eldar, Jan 29 2022 *)

a(n) = Sum_{k=1..n} A176031(k).

A351047 a(n) = Sum_{k=1..n} n^rad(k).

Original entry on oeis.org

1, 6, 39, 100, 3305, 54726, 958447, 2392776, 5375169, 10011102310, 311270518031, 804967791420, 304805198256481, 11910060539653290, 469042238075266815, 1229501390272865296, 830281003630789139585, 2193053904527215207698, 1983916064827419873906079

Offset: 1

Wesley Ivan Hurt, Jan 30 2022

nonn

			a(4) = 100; a(4) = Sum_{k=1..4} 4^rad(k) = 4^rad(1) + 4^rad(2) + 4^rad(3) + 4^rad(4) = 4^1 + 4^2 + 4^3 + 4^2 = 100.

Wikipedia, Radical of an integer.

Cf. A007947 (rad), A176031, A350996.

a[n_] := Sum[n^Times @@ FactorInteger[k][[;; , 1]], {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Feb 01 2022 *)

cp's OEIS Frontend

A350997 a(n) = Sum_{k=1..n} k^rad(k).

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