OFFSET
1,2
COMMENTS
Previous name was: Tetrahedral numbers ((k^3-k)/6) which are coprime to each smaller number in this sequence.
Sierpinski proved that any finite set of pairwise coprime tetrahedral numbers can be extended by adding an additional tetrahedral number which is coprime with all the elements of the set. Therefore this sequence is infinite. - Amiram Eldar, Mar 01 2019
REFERENCES
W. SierpiĆski, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970, Problem 43.
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..1000
EXAMPLE
35 is a term because it is the least tetrahedral number after 4 which is coprime to 1 and 4.
MATHEMATICA
t[n_] := n (n + 1) (n +2)/6; s = {1}; While[Length[s] < 50, k = s[[-1]] + 1; While[Max[GCD[t[k], t /@ s]] > 1, k++]; AppendTo[s, k]]; t /@ s (* Amiram Eldar, Mar 01 2019 *)
PROG
(PARI) v=vector(1000); n=0; for(i=1, 540537, t=i*(i+1)*(i+2)/6; for(j=2, n, if(gcd(t, v[j])>1, next(2))); n++; v[n]=t); v \\ Donovan Johnson, Oct 10 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Shyam Sunder Gupta, Nov 19 2002
EXTENSIONS
Edited by Don Reble, Nov 03 2005
New name from Amiram Eldar, Mar 02 2019
STATUS
approved