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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.)