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A115856 First differences of A115855. 2
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 (list; graph; refs; listen; history; text; internal format)
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..27.

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.

Sequence in context: A123631 A228364 A018060 * A147007 A146937 A032231

Adjacent sequences:  A115853 A115854 A115855 * A115857 A115858 A115859

KEYWORD

nonn,more

AUTHOR

Reinhard Zumkeller, Feb 01 2006

EXTENSIONS

More terms from Michael De Vlieger, Jul 15 2016

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)