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

%I A212197 #15 Aug 16 2021 21:36:27
%S A212197 1,2,6,14,42,114,602,798,1806,5334,34314,101346,229362,4357878,
%T A212197 9786714,12198858,168241542,185947566,231778302,524550894
%N A212197 Numbers k that divide the 3k-th Clausen number.
%C A212197 The classical Clausen numbers are given in A141056. See A160014 for generalizations. Related sequences are A014117 and A106741.
%H A212197 Thomas Clausen, <a href="http://adsabs.harvard.edu/abs/1840AN.....17R.351">Theorem. Lehrsatz aus einer Abhandlung ueber die Bernoullischen Zahlen</a>, Astr. Nachr. 17 (22) (1840), 351-352.
%t A212197 (* 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 *)
%o A212197 (PARI)
%o A212197 A212197_list(searchlimit) =
%o A212197 {
%o A212197     for (n=1, searchlimit,
%o A212197         p = 1;
%o A212197         fordiv(3*n, d,
%o A212197             r = d + 1;
%o A212197             if (isprime(r), p = p*r;)
%o A212197         );
%o A212197         if (Mod(p, n) == 0, print1(n, ", "));
%o A212197     );
%o A212197 }
%Y A212197 Cf. A014117, A027760, A106741, A141056, A160014.
%K A212197 nonn,more
%O A212197 1,2
%A A212197 _Peter Luschny_, May 05 2012