%I #25 Sep 14 2023 13:45:04

%S 1,1,1,4,1,1,1,4,1,1,1,4,1,1,1,16,1,1,1,4,1,1,1,4,1,1,27,4,1,1,1,16,1,

%T 1,1,4,1,1,1,4,1,1,1,4,1,1,1,16,1,1,1,4,1,27,1,4,1,1,1,4,1,1,1,64,1,1,

%U 1,4,1,1,1,4,1,1,1,4,1,1,1,16,27,1,1,4,1,1,1,4,1,1,1,4,1,1,1,16,1,1,1,4,1,1,1,4,1,1,1,108,1,1,1,16

%N Multiplicative with a(p^e) = p^(e-(e mod p)).

%C Fixed points of the map x -> gcd(x, A003415(x)), i.e., if we start iterating with A085731 from any x = n (>= 1), we will eventually reach a(n), after which the result does not change anymore. This was found by LODA miner (see C. Krause link), and is easily seen to be true by _Eric M. Schmidt_'s multiplicative formula for A085731. Note also that this sequence is idempotent, meaning a(a(n)) = a(n) for all n. - _Antti Karttunen_, Apr 05 2021

%C The largest divisor of n that is a term of A072873. - _Amiram Eldar_, Sep 14 2023

%H Antti Karttunen, <a href="/A327939/b327939.txt">Table of n, a(n) for n = 1..65537</a>

%H Christian Krause, <a href="https://github.com/ckrause/loda">LODA, an assembly language, a computational model and a tool for mining integer sequences</a>.

%F Multiplicative with a(p^e) = p^(e-(e mod p)).

%F a(n) = n / A327938(n).

%t f[p_, e_] := p^(e - Mod[e, p]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 14 2023 *)

%o (PARI) A327939(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]-(f[k,2]%f[k,1]))); factorback(f); };

%Y Cf. A003415, A072873, A085731, A327938.

%Y Differs from A234957 for the first time at n=27.

%K nonn,easy,mult

%O 1,4

%A _Antti Karttunen_, Oct 01 2019