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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
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<n, 0,
(t-> `if`(i<n, b(n-i, min(i-1, n-i), t), 0)
+`if`(i=n, t, 0)+b(n, i-1, r))(igcd(i, r)))
end:
a:= n-> 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
Sequence in context: A155722 A049045 A153766 * A093013 A272999 A278490
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 16 2018
STATUS
approved

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