A212197 Numbers k that divide the 3k-th Clausen number.

1, 2, 6, 14, 42, 114, 602, 798, 1806, 5334, 34314, 101346, 229362, 4357878, 9786714, 12198858, 168241542, 185947566, 231778302, 524550894

Offset: 1

Author

Peter Luschny, May 05 2012

Keywords

• nonn
• more

Comments

The classical Clausen numbers are given in A141056. See A160014 for generalizations. Related sequences are A014117 and A106741.

Links

• Thomas Clausen, Theorem. Lehrsatz aus einer Abhandlung ueber die Bernoullischen Zahlen, Astr. Nachr. 17 (22) (1840), 351-352.

Crossrefs

Cf. A014117, A027760, A106741, A141056, A160014.

Programs

Mathematica

(* This program is not convenient for more than 15 terms *) c[n_] := Sum[Boole[PrimeQ[d+1]]/(d+1), {d, Divisors[n]}] // Denominator; Reap[For[n = 1, n < 10^7, n++, If[Divisible[c[3*n], n], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, May 21 2013 *)

PARI

A212197_list(searchlimit) =
{
    for (n=1, searchlimit,
        p = 1;
        fordiv(3*n, d,
            r = d + 1;
            if (isprime(r), p = p*r;)
        );
        if (Mod(p, n) == 0, print1(n, ", "));
    );
}