A255602 -id:A255602 - cp's OEIS frontend

A253598 a(n) = least Lucas-Carmichael number which is divisible by b(n), where {b(n)} (A255602) is the list of all numbers which could be a divisor of a Lucas-Carmichael number.

399, 399, 935, 399, 935, 2015, 935, 399, 399, 4991, 51359, 2015, 8855, 1584599, 9486399, 20705, 5719, 18095, 2915, 935, 399, 46079, 162687, 2015, 22847, 46079, 16719263, 8855, 12719, 7055, 935, 80189, 189099039, 104663, 20705, 482143, 196559, 60059, 30073928079, 90287, 8855, 31535

Offset: 1

Tim Johannes Ohrtmann, Jan 05 2015

nonn

a(933) <= 266336887317945807999. - Daniel Suteu, Dec 01 2023

			a(12) = 8855 because this is the least Lucas-Carmichael number which is divisible by A255602(12) = 35.

Daniel Suteu, Table of n, a(n) for n = 1..932 (first 95 terms from Tim Johannes Ohrtmann, terms 96..154 from Robert G. Wilson v)

Cf. A006972, A253597, A255602.

LucasCarmichaelQ[n_] := Block[{fi = FactorInteger@ n}, ! PrimeQ@ n && Times @@ (Last@# & /@ fi) == 1 && Plus @@ Mod[n + 1, 1 + First@# & /@ fi] == 0]; LucasCarmichaelQ[1] = False; fQ[n_] := Block[{fi = FactorInteger@ n}, ffi = First@# & /@ fi; Times @@ (Last@# & /@ fi) == 1 && Min@ Flatten@ Table[Mod[1 + ffi, i], {i, ffi}] > 0]; fQ[1] = True; fQ[2] = False; lcdv = Select[ Range@ 3204, fQ]; f[n_] := Block[{k = lcdv[[n]]}, d = 2k; While[ !LucasCarmichaelQ@ k, k += d]; k]; Array[f, 95] (* Robert G. Wilson v, Feb 11 2015 *)

a(96) from Charles R Greathouse IV, Feb 12 2015

A306695 a(n) = gcd(n, psi(n)).

Original entry on oeis.org

1, 1, 1, 2, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 8, 1, 18, 1, 4, 1, 2, 1, 24, 5, 2, 9, 4, 1, 6, 1, 16, 3, 2, 1, 36, 1, 2, 1, 8, 1, 6, 1, 4, 9, 2, 1, 48, 7, 10, 3, 4, 1, 54, 1, 8, 1, 2, 1, 12, 1, 2, 3, 32, 1, 6, 1, 4, 3, 2, 1, 72, 1, 2, 15, 4, 1, 6, 1, 16, 27, 2, 1, 12, 1, 2, 3, 8, 1, 18, 7, 4, 1, 2, 5, 96, 1, 14, 9, 20

Offset: 1

Torlach Rush, Mar 05 2019

nonn

Here psi(n) is Dedekind's psi function A001615.
a(n) <= n <= A001615(n).
a(n) = n iff a(n) * 2 = A001615(n), n > 1.
a(n) = 1 iff either n=2 or n is in A255602. - Robert Israel, Mar 12 2019

Robert Israel, Table of n, a(n) for n = 1..10000
Wikipedia, Dedekind psi function

Cf. A001615, A255602.

f:= proc(n) local p; igcd(n, n*mul(1+1/p, p=numtheory:-factorset(n))) end proc:
map(f, [$1..100]); # Robert Israel, Mar 11 2019

psi[n_] := If[n == 1, 1, n Times @@ (1 + 1/FactorInteger[n][[All, 1]])];
a[n_] := GCD[n, psi[n]];
Array[a, 100] (* Jean-François Alcover, Jun 08 2020 *)

dpsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615
a(n) = gcd(n, dpsi(n)); \\ Michel Marcus, Mar 05 2019

a(n) = gcd(n, A001615(n)).

cp's OEIS Frontend

A253598 a(n) = least Lucas-Carmichael number which is divisible by b(n), where {b(n)} (A255602) is the list of all numbers which could be a divisor of a Lucas-Carmichael number.

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