A364501 a(n) = n / gcd(n, A005940(n)).

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, 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, 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

Offset

1,7

Comments

Numerator of n / A005940(n).

Links

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

Index entries for sequences related to binary expansion of n

Mathematica

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 *)

Prog

(PARI)
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A364501(n) = (n / gcd(n, A005940(n)));
(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); };

Crossrefs

Cf. A005940, A364500, A364502 (denominators), A364544 (positions of 1's).

Cf. also A364491.

Sequence in context: A370467 A164003 A280704 * A069609 A019855 A200288

Adjacent sequences: A364498 A364499 A364500 * A364502 A364503 A364504

Keyword

nonn,frac

Author

Antti Karttunen, Jul 28 2023

Status

approved