A355261 a(n) = largest-nth-power(n, 2) * radical(n) = A000188(n) * A007947(n), where largest-nth-power(n, e) is the largest positive integer b such that b^e divides n.

1, 2, 3, 4, 5, 6, 7, 4, 9, 10, 11, 12, 13, 14, 15, 8, 17, 18, 19, 20, 21, 22, 23, 12, 25, 26, 9, 28, 29, 30, 31, 8, 33, 34, 35, 36, 37, 38, 39, 20, 41, 42, 43, 44, 45, 46, 47, 24, 49, 50, 51, 52, 53, 18, 55, 28, 57, 58, 59, 60, 61, 62, 63, 16, 65, 66, 67, 68

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = p^(1+floor(e/2)). - Amiram Eldar, Jul 13 2022

Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(3)/2) * Product_{p prime} (1 - 2/p^3 + 1/p^4) = 0.447583182004... . - Amiram Eldar, Nov 13 2022

Maple

with(NumberTheory): seq(LargestNthPower(n, 2)*Radical(n), n = 1..68);

Mathematica

Array[Apply[Times, #[[All, 1]]]*Apply[Times, #1^Floor[#2/2] & @@ Transpose@ #] &@ FactorInteger[#] &, 68] (* Michael De Vlieger, Jul 12 2022 *)

Prog

(Python)
from math import prod
from sympy import factorint
def A355261(n): return prod(p**((e>>1)+1) for p, e in factorint(n).items()) # Chai Wah Wu, Jul 13 2022

Crossrefs

Cf. A000188, A002117, A007947, A064549, A355263.

Sequence in context: A083501 A007922 A007948 * A353897 A366905 A348262

Adjacent sequences: A355258 A355259 A355260 * A355262 A355263 A355264

Keyword

nonn,mult

Author

Peter Luschny, Jul 12 2022

Status

approved