A306414 a(n) = psi(A002997(n)), psi = A002322.

80, 48, 36, 112, 60, 1320, 198, 504, 360, 180, 120, 288, 1224, 2024, 36, 240, 300, 720, 72, 2320, 60, 108, 600, 112, 216, 1980, 8568, 528, 420, 6120, 2268, 360, 540, 3360, 240, 4900, 2160, 396, 432, 144, 300, 120, 576, 2970, 612, 396, 648, 630, 1260, 1080, 1008

Offset: 1

Author

Jianing Song, Feb 13 2019

Keywords

• nonn

Comments

By definition, A002997 lists the composite numbers k such that psi(k) divides k - 1. This sequence lists the values for psi(k) when k runs through A002997.

Examples

			A002997(1) = 561, psi(561) = 80, 561 = 7*80 + 1.
A002997(2) = 1105, psi(1105) = 48, 1105 = 23*48 + 1.
A002997(3) = 1729, psi(1729) = 36, 1729 = 48*36 + 1.
A002997(4) = 2465, psi(2465) = 112, 2465 = 22*112 + 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002997, A002322, A174590.

Programs

Mathematica

seq[kmax_] := Module[{s = {}, lam}, Do[If[CompositeQ[k], lam = CarmichaelLambda[k]; If[Mod[k, lam] == 1, AppendTo[s, lam]]], {k, 9, kmax, 2}]; s]; seq[10^6] (* Amiram Eldar, Nov 14 2023 *)

PARI

forstep(n=3, 1e6, 2, my(m=lcm(znstar(n)[2])); if((n-1)%m==0 && !isprime(n), print1(m, ", ")))

Formula

a(n) = A002322(A002997(n)).

a(n) = (A002997(n) - 1) / A174590(n). - Jianing Song, Dec 12 2021