The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A219107 Number of compositions (ordered partitions) of n into distinct prime parts. 18
 1, 0, 1, 1, 0, 3, 0, 3, 2, 2, 8, 1, 8, 3, 8, 8, 10, 25, 16, 9, 16, 38, 16, 61, 18, 62, 46, 66, 160, 91, 138, 99, 70, 122, 306, 126, 314, 151, 362, 278, 588, 901, 602, 303, 654, 1142, 888, 1759, 892, 1226, 950, 2160, 1230, 3379, 1444, 2372, 2100, 4644, 7416 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS a(0) = 0 iff n in {1,4,6}. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA a(n) = Sum_{k=0..A024936(n)} A219180(n,k)*k!. EXAMPLE a(5) = 3: [2,3], [3,2], [5]. a(7) = 3: [2,5], [5,2], [7]. a(8) = 2: [3,5], [5,3]. a(9) = 2: [2,7], [7,2]. a(10) = 8: [2,3,5], [2,5,3], [3,2,5], [3,5,2], [5,2,3], [5,3,2], [3,7], [7,3]. MAPLE with(numtheory): b:= proc(n, i) b(n, i):=       `if`(n=0, [1], `if`(i<1, [], zip((x, y)->x+y, b(n, i-1),        [0, `if`(ithprime(i)>n, [], b(n-ithprime(i), i-1))[]], 0)))     end: a:= proc(n) local l; l:= b(n, pi(n));       a(n):= add(l[i]*(i-1)!, i=1..nops(l))     end: seq(a(n), n=0..70); # second Maple program: s:= proc(n) option remember; `if`(n<1, 0, ithprime(n)+s(n-1)) end: b:= proc(n, i, t) option remember; `if`(s(i)`if`(p>n, 0, b(n-p, i-1, t+1)))(ithprime(i))+b(n, i-1, t)))     end: a:= n-> b(n, numtheory[pi](n), 0): seq(a(n), n=0..70);  # Alois P. Heinz, Jan 30 2020 MATHEMATICA zip = With[{m=Max[Length[#1], Length[#2]]}, PadRight[#1, m]+PadRight[#2, m] ]&; b[n_, i_] := b[n, i] = If[n==0, {1}, If[i<1, {}, b[n, i-1] ~zip~ Join[{0}, If[Prime[i] > n, {}, b[n - Prime[i], i-1]]], {0}]]; a[n_] := Module[{l}, l = b[n, PrimePi[n]]; Sum[l[[i]]*(i-1)!, {i, 1, Length[l]}]]; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Mar 24 2017, adapted from Maple *) CROSSREFS Cf. A000142, A000586, A032021, A218396. Sequence in context: A070298 A024938 A332715 * A338498 A221166 A004604 Adjacent sequences:  A219104 A219105 A219106 * A219108 A219109 A219110 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 11 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)