The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319301 Sum of GCDs of strict integer partitions of n. 4
 1, 2, 4, 5, 7, 10, 11, 14, 18, 21, 22, 33, 30, 39, 49, 54, 54, 78, 72, 100, 110, 121, 126, 181, 174, 207, 238, 284, 284, 389, 370, 466, 512, 582, 647, 806, 796, 954, 1066, 1265, 1300, 1616, 1652, 1979, 2192, 2452, 2636, 3202, 3336, 3892, 4237, 4843, 5172, 6090 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Wikipedia, Partition (number theory) FORMULA From Richard L. Ollerton, May 06 2021: (Start) a(n) = Sum_{d|n} A000010(n/d)*A000009(d). a(n) = Sum_{k=1..n} A000009(gcd(n,k)). a(n) = Sum_{k=1..n} A000009(n/gcd(n,k))*A000010(gcd(n,k))/A000010(n/gcd(n,k)). (End) MAPLE b:= proc(n, i, r) option remember; `if`(i*(i+1)/2 `if`(i b(n\$2, 0): seq(a(n), n=1..61); # Alois P. Heinz, Mar 17 2019 MATHEMATICA Table[Sum[GCD@@ptn, {ptn, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 30}] (* Second program: *) b[n_, i_, r_] := b[n, i, r] = If[i(i+1)/2 < n, 0, With[{t = GCD[i, r]}, If[i < n, b[n - i, Min[i - 1, n - i], t], 0] + If[i == n, t, 0] + b[n, i - 1, r]]]; a[n_] := b[n, n, 0]; Array[a, 61] (* Jean-François Alcover, May 20 2021, after Alois P. Heinz *) CROSSREFS Cf. A000009, A000010, A078374, A078392, A289508, A289509, A303138, A306956, A319300. Sequence in context: A155722 A049045 A153766 * A093013 A272999 A278490 Adjacent sequences: A319298 A319299 A319300 * A319302 A319303 A319304 KEYWORD nonn AUTHOR Gus Wiseman, Sep 16 2018 STATUS approved

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

Last modified June 19 17:03 EDT 2024. Contains 373504 sequences. (Running on oeis4.)