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A126773 a(n) = largest divisor of n which is coprime to the largest proper divisor of n. (a(1)=1.). 5
1, 2, 3, 1, 5, 2, 7, 1, 1, 2, 11, 1, 13, 2, 3, 1, 17, 2, 19, 1, 3, 2, 23, 1, 1, 2, 1, 1, 29, 2, 31, 1, 3, 2, 5, 1, 37, 2, 3, 1, 41, 2, 43, 1, 1, 2, 47, 1, 1, 2, 3, 1, 53, 2, 5, 1, 3, 2, 59, 1, 61, 2, 1, 1, 5, 2, 67, 1, 3, 2, 71, 1, 73, 2, 3, 1, 7, 2, 79, 1, 1, 2, 83, 1, 5, 2, 3, 1, 89, 2, 7, 1, 3, 2, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also the denominator of the ratio of the largest proper divisor to the least prime divisor of n, which can be thought of as the ratio of the 2nd largest divisor to the 2nd least divisor of n. - Michel Marcus, Feb 27 2017
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
For n >= 2: Let p =A020639(n) be the smallest prime dividing n. If p^2 divides n, then a(n)=1. Otherwise, a(n) = p.
EXAMPLE
The largest proper divisor of 30 is A032742(30) = 15. So a(30)= 2, because 2 is the largest divisor of 30 which is coprime to 15.
MAPLE
A126773 := proc(n)
local p ;
p := A020639(n) ;
if modp(n, p^2) = 0 then
1 ;
else
p ;
end if;
end proc:
seq(A126773(n), n=1..100) ; # R. J. Mathar, Mar 03 2017
MATHEMATICA
f[n_] := Block[{d = Divisors[n]}, If[n < 2, 1, Max @@ Select[d, GCD[ #, d[[ -2]]] == 1 &]]]; Array[f, 100] (* Ray Chandler, Feb 26 2007 *)
PROG
(PARI) a(n) = if (n==1, 1, my(d = divisors(n)); k = #d; while (gcd(d[k], d[#d-1]) != 1, k--); d[k]); \\ Michel Marcus, Feb 27 2017
(PARI) a(n) = if (n==1, 1, my(d = divisors(n)); denominator(d[#d-1]/d[2])); \\ Michel Marcus, Feb 27 2017
(PARI) a(n)=if(n==1, return(1)); my(f=factor(n)[1, ]); if(f[2]>1, 1, f[1]) \\ Charles R Greathouse IV, Feb 27 2017
CROSSREFS
Sequence in context: A055023 A323071 A340078 * A353274 A326691 A277698
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 17 2007
EXTENSIONS
Extended by Ray Chandler, Feb 26 2007
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)