This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115856 #17 Dec 12 2024 11:09:00
%S A115856 1,2,3,6,9,14,23,48,82,55,250,100,469,2213,2232,296,6623,489,29495,
%T A115856 89362,35815,1254,259171,411355,176134,952660,3819125,4564,9371908,
%U A115856 6841,13668113,47144847,6769988,403602715,672086464,21636,53588139,1454972415,6300092899,44582
%N A115856 First differences of A115855.
%C A115856 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 A115856 a(n) = A115855(n+1) - A115855(n).
%F A115856 a(A000040(n)-1) = A000041(A000040(n)) - 1.
%t A115856 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 A115856 Cf. A116085, A119983.
%K A115856 nonn
%O A115856 1,2
%A A115856 _Reinhard Zumkeller_, Feb 01 2006
%E A115856 a(20)-a(27) from _Michael De Vlieger_, Jul 15 2016
%E A115856 More terms from _Jinyuan Wang_, Dec 12 2024