A318786 - OEIS

%I #25 Nov 23 2018 05:27:49

%S 2,3,5,11,17,29,37,41,61,67,73,97,101,107,109,113,131,137,149,157,181,

%T 193,197,211,227,233,241,257,269,277,281,307,317,331,337,347,353,373,

%U 389,397,401,409,421,457,461,467,491,521,541,547,557,569,577,587,601,613,617,641

%N Primes p such that the only term of A000292 that divides A000292(p) is A000292(1).

%C a(2) = 3 does not divide A000292(a(2)).

%C A000292(a(n)) = a(n) * k, n <> 2, k > 1.

%e 2 is a term because A000292(2)=4 is only divisible by A000292(1)=1.

%e 3 is a term because A000292(3)=10 is only divisible by A000292(1)=1.

%e 7 is not a term because A000292(7)=84 is divisible by A000292(2)=4.

%t t[n_] := n(n+1)(n+2)/6; seqQ[n_] := If[PrimeQ[n], Module[{tn = t[n], ans = True}, Do[If[Divisible[tn, t[i]], ans=False; Break[]], {i, 2, n-1}]; ans], False]; Select[Range[650], seqQ] (* _Amiram Eldar_, Nov 22 2018 *)

%o (PARI) t(n) = n*(n+1)*(n+2)/6;

%o isok(n) = if (isprime(n), my(tn = t(n)); for (i=2, n-1, if ((tn % t(i)) == 0, return (0))); return (1), return (0)); \\ _Michel Marcus_, Sep 23 2018

%Y Cf. A000292 (tetrahedral numbers), A317986 (corresponding tetrahedral numbers).

%K nonn

%O 1,1

%A _Torlach Rush_, Sep 03 2018