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.

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, 14, 29, 30, 31, 4, 33, 34, 35, 6, 37, 38, 39, 20, 41, 42, 43, 22, 15, 46, 47, 12, 7, 10, 51, 26, 53, 18, 55, 28, 57, 58, 59, 30, 61, 62, 21, 8, 65, 66, 67, 34, 69

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = p^(1 + floor(e/3)). - Amiram Eldar, Jul 13 2022

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

Maple

with(NumberTheory): seq(LargestNthPower(n, 3)*Radical(n), n=1..69);

Mathematica

f[p_, e_] := p^(1 + Floor[e/3]); a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 13 2022 *)

Prog

(Python)
from math import prod
from sympy import factorint
def A355263(n): return prod(p**(e//3+1) for p, e in factorint(n).items()) # Chai Wah Wu, Jul 13 2022

Crossrefs

Cf. A000188, A013663, A053150, A064549, A355261.

Sequence in context: A375240 A066069 A019530 * A019554 A371573 A076685

Adjacent sequences: A355260 A355261 A355262 * A355264 A355265 A355266

Keyword

nonn,mult

Author

Peter Luschny, Jul 12 2022

Status

approved