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A209122 Numbers a(n) for which there exists k>1 such that the number of partitions of a(n) into k parts is k. 0
4, 5, 6, 9, 12, 17, 22, 30, 39, 52, 67, 89, 114, 149, 191, 247, 314, 403, 509, 647, 813, 1024, 1278, 1599, 1983, 2462, 3037, 3746, 4594, 5634, 6873, 8381, 10176, 12344, 14918, 18013, 21674, 26053, 31224, 37378, 44624, 53216, 63304, 75219 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For n>2, k=a(n)-n.

LINKS

Table of n, a(n) for n=1..44.

FORMULA

a(1)=4, a(2)=5, and a(n)=n+A000041(n) if n>2; i.e., k(n)=A000041(n) for n>2.

EXAMPLE

The partitions of a(4)=9 into k=9-4 parts are

5+1+1+1+1, 4+2+1+1+1, 3+3+1+1+1, 3+2+3+1+1, 2+2+2+2+1.

MATHEMATICA

f[n_, k_] := Length[IntegerPartitions[n, {k}]]

t[n_] := Table[f[n, k] - k, {k, 1, n}]

b[n_] := Position[t[n], 0]

c = Flatten[Table[Last[b[n]], {n, 1, 60}]]

x = Flatten[Position[c, 1]]

y = Complement[Range[Length[x]], x]

CROSSREFS

Cf. A000041, A133041.

Sequence in context: A115984 A145025 A245236 * A064931 A073263 A039013

Adjacent sequences:  A209119 A209120 A209121 * A209123 A209124 A209125

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 05 2012

STATUS

approved

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Last modified May 22 13:18 EDT 2017. Contains 286872 sequences.