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!)
 A092309 Sum of smallest parts (counted with multiplicity) of all partitions of n. 13
 1, 4, 7, 15, 19, 39, 46, 80, 106, 160, 201, 318, 390, 554, 729, 998, 1262, 1727, 2168, 2894, 3670, 4749, 5963, 7737, 9635, 12232, 15257, 19206, 23727, 29723, 36509, 45296, 55512, 68292, 83298, 102079, 123805, 150697, 182254, 220790, 265766 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..9000 FORMULA G.f.: Sum(n*x^n/(1-x^n)*Product(1/(1-x^k), k = n .. infinity), n = 1 .. infinity). a(n) ~ sqrt(2) * exp(Pi*sqrt(2*n/3)) / (4*Pi*sqrt(n)). - Vaclav Kotesovec, Jul 06 2019 EXAMPLE Partitions of 4 are: [1,1,1,1], [1,1,2], [2,2], [1,3], [4]; thus a(4)=4*1+2*1+2*2+1*1+1*4=15. MAPLE b:= proc(n, i) option remember; `if`(irem(n, i)=0, n, 0)        +`if`(i>1, add(b(n-i*j, i-1), j=0..(n-1)/i), 0)     end: a:= n-> b(n\$2): seq(a(n), n=1..50);  # Alois P. Heinz, Feb 04 2016 MATHEMATICA ss[n_]:=Module[{m=Min[n]}, Select[n, #==m&]]; Table[Total[Flatten[ss/@ IntegerPartitions[n]]], {n, 50}] (* Harvey P. Dale, Dec 16 2013 *) b[n_, i_] := b[n, i] = If[Mod[n, i] == 0, n, 0] + If[i > 1, Sum[b[n - i*j, i - 1], {j, 0, (n - 1)/i}], 0]; a[n_] := b[n, n]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Aug 29 2016, after Alois P. Heinz *) CROSSREFS Cf. A092314, A092322, A092269, A092321, A092313, A092310, A092311, A092268. Cf. A046746. Sequence in context: A310926 A310927 A049832 * A263617 A271675 A039669 Adjacent sequences:  A092306 A092307 A092308 * A092310 A092311 A092312 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Feb 16 2004 EXTENSIONS More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004 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 April 18 22:28 EDT 2021. Contains 343090 sequences. (Running on oeis4.)