OFFSET
1,3
COMMENTS
No k exists precisely when n == 0 (mod 4).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = (n*A076107(n)+(n^2-n)/2)^(1/n) for n != 0 (mod 4).
a(n) = A076108^(1/n).
a(p) = p if p is a prime.
Multiplicative with a(2^1) = 1; a(2^e) = 0 if e >= 2; a(p^e) = p if p >= 3. - David W. Wilson, Jun 10 2005
a(n) = A007947(n) if n == 1 (mod 2); A007947(n/2) if n == 2 (mod 4); 0 if n == 0 (mod 4). - David W. Wilson, Jun 10 2005
a(4k) = 0; otherwise a(n) = p1*...*pm where p1, ..., pm are all distinct odd primes dividing n. - Max Alekseyev, Jun 10 2005
Sum_{k=1..n} a(k) ~ c * n^2, where c = (3/8) * Product_{p prime} (1 - 1/(p*(p+1))) = (3/8) * A065463 = 0.264165... . - Amiram Eldar, Oct 28 2022
MATHEMATICA
f[p_, e_] := If[p == 2, Boole[e == 1], p]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 09 2020 *)
PROG
(PARI) { A076109(n) = if(n%4==0, return(0)); if(n%2==0, n\=2); vecprod(factorint(n)[, 1]); } \\ Max Alekseyev, Jun 10 2005
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amarnath Murthy, Oct 08 2002
EXTENSIONS
Corrected and extended by Ralf Stephan, Mar 30 2003
More terms from Max Alekseyev, Jun 10 2005
STATUS
approved