A325147 Reduced Clausen numbers.

10, 546, 2, 46, 6630, 76670, 211659630, 6, 261870, 111418, 46, 13589784390, 524588442, 114, 1138240087314330, 2, 276742830, 26805565070, 1909802752494, 3210, 15370, 177430547680928732190, 358, 5760551069383110, 76004922, 1126, 4347631610092420338, 81366

Offset

1,1

Comments

Let P(m) denote the prime factors of m and C(m) = Clausen(m-1, 1) (cf. A160014) then Product_{p in P(C(m)) setminus P(m)} p is in this sequence provided P(m) is a subset of P(C(m)).

Links

Table of n, a(n) for n=1..28.

Example

Let n = 561 then P(561) = {3, 11, 17} and P(Clausen(560,1)) = {2, 3, 5, 11, 17, 29, 41, 71, 113, 281}. Since P(561) is a subset of P(Clausen(560, 1)), a(18) = 2*5*29*41*71*113*281 = 26805565070.

Maple

with(numtheory): a := proc(n) if isweakCarmichael(n) then # cf. A225498 and A160014
mul(m, m in factorset(Clausen(n-1, 1)) minus factorset(n)) else NULL fi end:
seq(a(n), n=2..1350);

Mathematica

pf[n_] := FactorInteger[n][[All, 1]];
Clausen[0, _] = 1; Clausen[n_, k_] := Times @@ (Select[Divisors[n], PrimeQ[# + k]&] + k);
weakCarmQ[n_] := If[EvenQ[n] || PrimeQ[n], Return[False], pf[n] == (pf[n] ~Intersection~ pf[Clausen[n - 1, 1]])];
f[n_] := Times @@ Complement[pf[Clausen[n - 1, 1]], pf[n]];
f /@ Select[Range[2, 2000], weakCarmQ] (* Jean-François Alcover, Jul 21 2019 *)

Crossrefs

Weak Carmichael numbers are A225498. Clausen numbers are in A160014.

A324977 is a subsequence.

Sequence in context: A180359 A289200 A014382 * A370733 A035308 A327412

Adjacent sequences: A325144 A325145 A325146 * A325148 A325149 A325150

Keyword

nonn

Author

Peter Luschny, May 21 2019

Status

approved