A115856 First differences of A115855.

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

1,2

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

Links

Table of n, a(n) for n=1..40.

Formula

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

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

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 *)

Crossrefs

Cf. A116085, A119983.

Sequence in context: A123631 A228364 A018060 * A147007 A146937 A032231

Adjacent sequences: A115853 A115854 A115855 * A115857 A115858 A115859

Keyword

nonn

Author

Reinhard Zumkeller, Feb 01 2006

Extensions

a(20)-a(27) from Michael De Vlieger, Jul 15 2016

More terms from Jinyuan Wang, Dec 12 2024

Status

approved