A364500 a(n) = gcd(n, A005940(n)).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jul 28 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A005940, A364499, A364501, A364502.

Cf. also A324198, A339969, A364255.

Programs

Mathematica

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 *)

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A364500(n) = gcd(n, A005940(n));

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); };

Formula

a(n) = gcd(n, A364499(n)) = gcd(A005940(n), A364499(n)).

a(n) = n / A364501(n) = A005940(n) / A364502(n).