A356489 a(n) = A000265(rad(prime(n)-1)), rad = A007947.

1, 1, 1, 3, 5, 3, 1, 3, 11, 7, 15, 3, 5, 21, 23, 13, 29, 15, 33, 35, 3, 39, 41, 11, 3, 5, 51, 53, 3, 7, 21, 65, 17, 69, 37, 15, 39, 3, 83, 43, 89, 15, 95, 3, 7, 33, 105, 111, 113, 57, 29, 119, 15, 5, 1, 131, 67, 15, 69, 35, 141, 73, 51, 155, 39, 79, 165, 21, 173, 87, 11, 179

Offset

1,4

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000265(rad(prime(n)-1)) = rad(A000265(prime(n)-1)).

a(n) = Product_{odd primes p dividing prime(n)-1} p.

a(n) = A000265(A077063(n)) = rad(A057023(n)) = A204455(prime(n)-1).

Example

prime(8) = 19, so a(8) = A000265(rad(18)) = A000265(6) = 3.
prime(11) = 31, so a(11) = A000265(rad(30)) = A000265(30) = 15.

Mathematica

Array[#/2^IntegerExponent[#, 2] &[Times @@ FactorInteger[Prime[#] - 1][[All, 1]]] &, 72] (* Michael De Vlieger, Aug 09 2022 *)

Prog

(PARI) a(n) = factorback(setminus(factorint(prime(n)-1)[, 1]~, [2]))

Crossrefs

Cf. A000265, A007947, A077063, A057023, A204455.

Sequence in context: A241014 A173454 A023505 * A196997 A254934 A021743

Adjacent sequences: A356486 A356487 A356488 * A356490 A356491 A356492

Keyword

nonn,easy

Author

Jianing Song, Aug 09 2022

Status

approved