A364502 a(n) = A005940(n) / gcd(n, A005940(n)).

1, 1, 1, 1, 1, 1, 9, 1, 7, 1, 15, 1, 25, 9, 9, 1, 11, 7, 21, 1, 5, 15, 45, 1, 49, 25, 25, 9, 125, 9, 81, 1, 13, 11, 33, 7, 55, 21, 21, 1, 77, 5, 105, 15, 35, 45, 135, 1, 121, 49, 49, 25, 245, 25, 45, 9, 343, 125, 375, 9, 625, 81, 27, 1, 17, 13, 39, 11, 65, 33, 99, 7, 91, 55, 11, 21, 25, 21, 189, 1, 143, 77, 231, 5

Offset: 1

Author

Antti Karttunen, Jul 28 2023

Keywords

• nonn
• frac

Comments

Denominator of n / A005940(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A005940, A364500, A364501 (numerators), A364546 (positions of 1's).

Cf. also A364492.

Programs

Mathematica

nn = 84; 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[a[#]/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 };
A364502(n) = { my(u=A005940(n)); (u / gcd(n, u)); };