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a(n) = psi(A002997(n)), psi = A002322.
4

%I #20 Nov 14 2023 04:36:47

%S 80,48,36,112,60,1320,198,504,360,180,120,288,1224,2024,36,240,300,

%T 720,72,2320,60,108,600,112,216,1980,8568,528,420,6120,2268,360,540,

%U 3360,240,4900,2160,396,432,144,300,120,576,2970,612,396,648,630,1260,1080,1008

%N a(n) = psi(A002997(n)), psi = A002322.

%C 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.

%H Amiram Eldar, <a href="/A306414/b306414.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = (A002997(n) - 1) / A174590(n). - _Jianing Song_, Dec 12 2021

%e A002997(1) = 561, psi(561) = 80, 561 = 7*80 + 1.

%e A002997(2) = 1105, psi(1105) = 48, 1105 = 23*48 + 1.

%e A002997(3) = 1729, psi(1729) = 36, 1729 = 48*36 + 1.

%e A002997(4) = 2465, psi(2465) = 112, 2465 = 22*112 + 1.

%t 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 *)

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

%Y Cf. A002997, A002322, A174590.

%K nonn

%O 1,1

%A _Jianing Song_, Feb 13 2019