cp's OEIS Frontend

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.

A115856 First differences of A115855.

Original entry on oeis.org

1, 2, 3, 6, 9, 14, 23, 48, 82, 55, 250, 100, 469, 2213, 2232, 296, 6623, 489, 29495, 89362, 35815, 1254, 259171, 411355, 176134, 952660, 3819125, 4564, 9371908, 6841, 13668113, 47144847, 6769988, 403602715, 672086464, 21636, 53588139, 1454972415, 6300092899, 44582
Offset: 1

Views

Author

Reinhard Zumkeller, Feb 01 2006

Keywords

Comments

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

Crossrefs

Programs

  • Mathematica
    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 *)

Formula

a(n) = A115855(n+1) - A115855(n).
a(A000040(n)-1) = A000041(A000040(n)) - 1.

Extensions

a(20)-a(27) from Michael De Vlieger, Jul 15 2016
More terms from Jinyuan Wang, Dec 12 2024