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 A308833 Numbers r such that the r-th tetrahedral number A000292(r) divides r!. 1
 1, 7, 8, 13, 14, 19, 20, 23, 24, 25, 26, 31, 32, 33, 34, 37, 38, 43, 44, 47, 48, 49, 50, 53, 54, 55, 56, 61, 62, 63, 64, 67, 68, 73, 74, 75, 76, 79, 80, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 97, 98, 103, 104, 109, 110, 113, 114, 115, 116, 117, 118, 119, 120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: for every odd number r such that r > 1, the following four conditions are equivalent: a) r is a term of this sequence, b) r+1 is a term of this sequence, c) r+2 is composite. LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 EXAMPLE The 7th tetrahedral number is 84, and 84*60 = 5040 = 7!. MAPLE f:=proc(n) local i, S; S := {}: for i from 1 to n do if type(i!/(i*(i+1)*(i+2)/6), integer) then S :=`union`(S, {i}): end if: end do: return S; end proc: MATHEMATICA Select[Range@ 120, Mod[#!, Pochhammer[#, 3]/6] == 0 &] (* Michael De Vlieger, Jul 08 2019 *) PROG (PARI) isok(k) = !(k! % (k*(k+1)*(k+2)/6)); \\ Michel Marcus, Jun 28 2019 (PARI) is(n) = { my(f = factor(binomial(n + 2, 3))); forstep(i = #f~, 1, -1, if(val(n, f[i, 1]) - f[i, 2] < 0, return(0) ) ); 1 } val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Mar 22 2021 CROSSREFS Cf. A000142 (factorial numbers), A000292 (tetrahedral numbers). Cf. A007921 (numbers which are not difference of two primes), A153238. Sequence in context: A343298 A061905 A308887 * A025156 A228210 A045765 Adjacent sequences:  A308830 A308831 A308832 * A308834 A308835 A308836 KEYWORD nonn,easy AUTHOR Lorenzo Sauras Altuzarra, Jun 28 2019 STATUS approved

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Last modified June 16 02:14 EDT 2021. Contains 345055 sequences. (Running on oeis4.)