This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A212218 Number of representations of n as a sum of products of distinct pairs of positive integers, n = Sum_{k=1..m} i_k*j_k with i_k<=j_k, i_k
 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6, 5, 7, 7, 8, 9, 10, 9, 11, 12, 13, 14, 16, 14, 18, 21, 19, 20, 23, 23, 28, 28, 28, 30, 36, 33, 39, 42, 39, 44, 50, 46, 54, 57, 56, 62, 69, 64, 71, 77, 82, 85, 89, 84, 99, 107, 103, 111, 119, 117, 132, 137, 137, 142 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 EXAMPLE a(0) = 1: 0 = the empty sum. a(1) = 1: 1 = 1*1. a(4) = 2: 4 = 1*4 = 2*2. a(5) = 2: 5 = 1*1 + 2*2 = 1*5. a(9) = 3: 9 = 1*1 + 2*4 = 1*9 = 3*3. a(12) = 4: 12 = 1*2 + 2*5 = 1*12 = 2*6 = 3*4. a(15) = 5: 15 = 1*3 + 2*6 = 1*3 + 3*4 = 1*1 + 2*7 = 1*15 = 3*5. MAPLE with(numtheory): b:= proc(n, m, i, j) option remember;       `if`(n=0, 1, `if`(m<1, 0, b(n, m-1, i, j) +`if`(m>n, 0,         add(b(n-m, m-1, min(i, k-1), min(j, m/k-1)), k=select(x->          is(x<=min(sqrt(m), i) and m<=j*x), divisors(m))))))     end: a:= n-> b(n\$4): seq(a(n), n=0..30); MATHEMATICA b[n_, m_, i_, j_] := b[n, m, i, j] = If[n == 0, 1, If[m<1, 0, b[n, m-1, i, j]+If[m>n, 0, Sum[b[n-m, m-1, Min[i, k-1], Min[j, m/k-1]], {k, Select[Divisors[m], # <= Min[Sqrt[m], i] && m <= j*#&]}]]]]; a[n_] := b[n, n, n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 05 2014, after Alois P. Heinz *) CROSSREFS Cf. A066739, A182269, A182270, A211856, A211857, A212214, A212215, A212216, A212217, A212219. Sequence in context: A194304 A090701 A056970 * A321162 A008668 A225643 Adjacent sequences:  A212215 A212216 A212217 * A212219 A212220 A212221 KEYWORD nonn AUTHOR Alois P. Heinz, May 06 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 August 24 13:48 EDT 2019. Contains 326279 sequences. (Running on oeis4.)