OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p^(e+floor(e/2)). - Amiram Eldar, Jul 13 2022
From Amiram Eldar, Sep 21 2023: (Start)
Dirichlet g.f.: zeta(s-1) * zeta(2*s-3)/ zeta(2*s-2).
Sum_{k=1..n} a(k) ~ (3*n^2/(4*Pi^2)) * (2*log(n) + 6*gamma - 4*zeta'(2)/zeta(2) - 1), where gamma is Euler's constant (A001620). (End)
MAPLE
with(NumberTheory): seq(n*LargestNthPower(n, 2), n = 1..64);
MATHEMATICA
Table[n*Times @@ (#1^Floor[#2/2] & @@@ FactorInteger[n]), {n, 64}] (* Michael De Vlieger, Jul 12 2022 *)
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^(f[i, 2] + f[i, 2]\2)); } \\ Amiram Eldar, Sep 21 2023
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Peter Luschny, Jul 12 2022
STATUS
approved