A318786 Primes p such that the only term of A000292 that divides A000292(p) is A000292(1).

2, 3, 5, 11, 17, 29, 37, 41, 61, 67, 73, 97, 101, 107, 109, 113, 131, 137, 149, 157, 181, 193, 197, 211, 227, 233, 241, 257, 269, 277, 281, 307, 317, 331, 337, 347, 353, 373, 389, 397, 401, 409, 421, 457, 461, 467, 491, 521, 541, 547, 557, 569, 577, 587, 601, 613, 617, 641

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..58.

Example

2 is a term because A000292(2)=4 is only divisible by A000292(1)=1.
3 is a term because A000292(3)=10 is only divisible by A000292(1)=1.
7 is not a term because A000292(7)=84 is divisible by A000292(2)=4.

Mathematica

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 *)

Prog

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

Crossrefs

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

Sequence in context: A049565 A094480 A215013 * A038909 A073534 A063091

Adjacent sequences: A318783 A318784 A318785 * A318787 A318788 A318789

Keyword

nonn

Author

Torlach Rush, Sep 03 2018

Status

approved