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A209489 Number of partitions of 1 into rational parts a/b satisfying 0<a<b<=n. 2
0, 1, 3, 6, 12, 19, 33, 50, 77, 111, 166, 229, 329, 448, 615, 824, 1120, 1467, 1956, 2538, 3313, 4258, 5512, 6993, 8944, 11278, 14258, 17838, 22402, 27788, 34629, 42747, 52832, 64844, 79706, 97232, 118868, 144392, 175474, 212168, 256750 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..41.

FORMULA

a(n)=a(n-1)-1+(number of partitions of n into relatively prime parts).

EXAMPLE

a(1)=0.

a(2)=1 counts 1/2 + 1/2.

a(3)=3 counts 1/2 + 1/2, 1/3 + 1/3 + 1/3, and 1/3 + 2/3.

MATHEMATICA

p[n_] := p[n] = IntegerPartitions[n];

l[n_] := Length[p[n]];

p[n_, j_] := p[n, j] = Part[p[n], j]

g[n_, j_] := g[n, j] = Apply[GCD, p[n, j]]

h[n_] := h[n] = Table[g[n, j], {j, 1, l[n]}]

c[n_] := c[n] = Count[h[n], 1]

Table[c[n], {n, 0, 45}]      (* A000837 *)

s[n_] := Sum[c[k], {k, 1, n}]

Table[s[n] - 1, {n, 1, 45}]  (* A209489 *)

CROSSREFS

Cf. A000837.

Sequence in context: A263511 A180622 A125851 * A181962 A226220 A218076

Adjacent sequences:  A209486 A209487 A209488 * A209490 A209491 A209492

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 09 2012

STATUS

approved

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Last modified April 29 22:12 EDT 2017. Contains 285615 sequences.