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 A318786 Primes p such that the only term of A000292 that divides A000292(p) is A000292(1). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(2) = 3 does not divide A000292(a(2)). A000292(a(n)) = a(n) * k, n <> 2, k > 1. LINKS 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

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Last modified September 27 22:36 EDT 2020. Contains 337388 sequences. (Running on oeis4.)