cp's OEIS Frontend

A355263 a(n) = largest-nth-power(n, 3) * radical(n) = A053150(n) * A007947(n), where the largest-nth-power(n, e) is the largest positive integer b such that b^e divides n.

%I A355263 #22 Nov 13 2022 08:40:46
%S A355263 1,2,3,2,5,6,7,4,3,10,11,6,13,14,15,4,17,6,19,10,21,22,23,12,5,26,9,
%T A355263 14,29,30,31,4,33,34,35,6,37,38,39,20,41,42,43,22,15,46,47,12,7,10,51,
%U A355263 26,53,18,55,28,57,58,59,30,61,62,21,8,65,66,67,34,69
%N A355263 a(n) = largest-nth-power(n, 3) * radical(n) = A053150(n) * A007947(n), where the largest-nth-power(n, e) is the largest positive integer b such that b^e divides n.
%H A355263 Amiram Eldar, <a href="/A355263/b355263.txt">Table of n, a(n) for n = 1..10000</a>
%F A355263 Multiplicative with a(p^e) = p^(1 + floor(e/3)). - _Amiram Eldar_, Jul 13 2022
%F A355263 Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(5)/2) * Product_{p prime} (1 - 1/p^2 + 1/p^3 - 2/p^5 + 1/p^6) = 0.3643121583... . - _Amiram Eldar_, Nov 13 2022
%p A355263 with(NumberTheory): seq(LargestNthPower(n, 3)*Radical(n), n=1..69);
%t A355263 f[p_, e_] := p^(1 + Floor[e/3]); a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jul 13 2022 *)
%o A355263 (Python)
%o A355263 from math import prod
%o A355263 from sympy import factorint
%o A355263 def A355263(n): return prod(p**(e//3+1) for p, e in factorint(n).items()) # _Chai Wah Wu_, Jul 13 2022
%Y A355263 Cf. A000188, A013663, A053150, A064549, A355261.
%K A355263 nonn,mult
%O A355263 1,2
%A A355263 _Peter Luschny_, Jul 12 2022