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 #17 Dec 12 2024 11:09:00
%S 1,2,3,6,9,14,23,48,82,55,250,100,469,2213,2232,296,6623,489,29495,
%T 89362,35815,1254,259171,411355,176134,952660,3819125,4564,9371908,
%U 6841,13668113,47144847,6769988,403602715,672086464,21636,53588139,1454972415,6300092899,44582
%N First differences of A115855.
%C By definition of A115855, a(n+1) is the number of ways 1 can be written as sum of distinct positive fractions having no denominator larger than n, and at least one equal to n (in its reduced form). - _M. F. Hasler_, Jul 14 2016
%F a(n) = A115855(n+1) - A115855(n).
%F a(A000040(n)-1) = A000041(A000040(n)) - 1.
%t Table[Length@ Select[Flatten[Map[IntegerPartitions[1, {#}, Rest@ Union[Flatten@ TensorProduct[#, 1/#] &@ Range@ n /. {_Integer -> 0, k_ /; k > 1 -> 0}]] &, Range@ n], 1], Total@ # == 1 && MemberQ[Union@ Denominator@ #, n] &], {n, 2, 25}] (* _Michael De Vlieger_, Jul 15 2016 *)
%Y Cf. A116085, A119983.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Feb 01 2006
%E a(20)-a(27) from _Michael De Vlieger_, Jul 15 2016
%E More terms from _Jinyuan Wang_, Dec 12 2024