A212197 - OEIS

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

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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, ", "));

);