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%I #12 Jul 28 2023 15:53:06
%S 1,1,1,1,1,1,7,1,9,1,11,1,13,7,5,1,17,9,19,1,3,11,23,1,25,13,9,7,29,5,
%T 31,1,33,17,35,9,37,19,13,1,41,3,43,11,9,23,47,1,49,25,17,13,53,9,11,
%U 7,57,29,59,5,61,31,7,1,65,33,67,17,69,35,71,9,73,37,5,19,7,13,79,1,81,41,83,3,17,43,29,11,89
%N a(n) = n / gcd(n, A005940(n)).
%C Numerator of n / A005940(n).
%H Antti Karttunen, <a href="/A364501/b364501.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>
%t nn = 89; 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}], n]; 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 A364501(n) = (n / gcd(n, A005940(n)));
%o (PARI) A364501(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); (orgn/z); };
%Y Cf. A005940, A364500, A364502 (denominators), A364544 (positions of 1's).
%Y Cf. also A364491.
%K nonn,frac
%O 1,7
%A _Antti Karttunen_, Jul 28 2023
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