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

1,2

Comments

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

Links

Table of n, a(n) for n=1..20.

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

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 *)

Prog

(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, ", "));
    );
}

Crossrefs

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

Sequence in context: A123383 A281707 A225172 * A151414 A151386 A151399

Adjacent sequences: A212194 A212195 A212196 * A212198 A212199 A212200

Keyword

nonn,more

Author

Peter Luschny, May 05 2012

Status

approved