Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #7 Jun 02 2021 22:23:25
%S 2,15,7,2431,437,1363783,107113,1249792339,56606581,1741209542339,
%T 8811899415119,1107997261359193637,113411646442333,
%U 5544791201146623008917,785518504414223,88816991126218293876923,140194949408966090156937953,517859057576547860552412883,6474009927400912083137
%N Divide the positive integers into subsets of lengths given by successive primes. a(n) is the product of primes contained in the n-th subset.
%e a(1) = 2 because the first subset is [1,2] (length = 2) and the product of primes contained in it is 2.
%e a(2) = 15 because the second subset is [3,4,5] (length = 3) and the product of primes contained in it is 3 * 5 = 15.
%e a(3) = 7 because the third subset is [6,7,8,9,10] (length = 5) and the product of primes contained in it is 7.
%e a(4) = 2431 because the fourth subset is [11,12,13,14,15,16,17] (length = 7) and the product of primes contained in it is 11 * 13 * 17 = 2431.
%t nterms=100;list = TakeList[Range[Sum[Prime[i],{i,nterms}]],Prime[Range[nterms]]];listprime=Map[Select[#,PrimeQ]&,list];Map[Apply[Times,#]&,listprime]
%Y Cf. A000040, A002110, A344718.
%K nonn
%O 1,1
%A _Paolo Xausa_, Jun 01 2021