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%I #14 Jul 28 2023 15:53:03
%S 1,2,3,4,5,6,1,8,1,10,1,12,1,2,3,16,1,2,1,20,7,2,1,24,1,2,3,4,1,6,1,
%T 32,1,2,1,4,1,2,3,40,1,14,1,4,5,2,1,48,1,2,3,4,1,6,5,8,1,2,1,12,1,2,9,
%U 64,1,2,1,4,1,2,1,8,1,2,15,4,11,6,1,80,1,2,1,28,5,2,3,8,1,10,7,4,1,2,5,96,1,2,33,4
%N a(n) = gcd(n, A005940(n)).
%H Antti Karttunen, <a href="/A364500/b364500.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(n) = gcd(n, A364499(n)) = gcd(A005940(n), A364499(n)).
%F a(n) = n / A364501(n) = A005940(n) / A364502(n).
%t nn = 100; Array[Set[a[#], #] &, 2]; Do[If[EvenQ[n], Set[a[n], 2 a[n/2]], Set[a[n], Times @@ Power @@@ Map[{Prime[PrimePi[#1] + 1], #2} & @@ # &, FactorInteger[a[(n + 1)/2]]]]], {n, 3, nn}]; Array[GCD[a[#], #] &, nn] (* _Michael De Vlieger_, Jul 28 2023 *)
%o (PARI)
%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A364500(n) = gcd(n, A005940(n));
%o (PARI) A364500(n) = { my(orgn=n,p=2,rl=0,z=1); n--; while(n, if(!(n%2), p=nextprime(1+p), rl++; if(1==(n%4), z *= p^min(rl,valuation(orgn,p)); rl=0)); n>>=1); (z); };
%Y Cf. A005940, A364499, A364501, A364502.
%Y Cf. also A324198, A339969, A364255.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 28 2023
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