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A227296 Number of partitions of n into parts <= phi(n), where phi is Euler's totient function (cf. A000010). 3
1, 1, 1, 2, 3, 6, 4, 14, 15, 26, 23, 55, 34, 100, 90, 146, 186, 296, 199, 489, 434, 725, 807, 1254, 919, 1946, 2063, 2943, 3036, 4564, 2462, 6841, 7665, 9871, 11098, 14744, 12384, 21636, 23928, 30677, 31603, 44582, 31570, 63260, 69414, 86420, 99795, 124753 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)*n). - Vaclav Kotesovec, May 24 2018

MAPLE

with(numtheory):

b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,

       b(n, i-1) +`if`(i>n, 0, b(n-i, i)))

    end:

a:= n-> b(n, phi(n)):

seq(a(n), n=0..100);  # Alois P. Heinz, May 11 2015

MATHEMATICA

(* Requires version 6.0+ *) Table[Length[IntegerPartitions[n, n, Range[EulerPhi[n]]]], {n, 0, 47}] (* Ivan Neretin, May 11 2015 *)

intPartLen[n_, i_] := intPartLen[n, i] = If[n == 0 || i == 1, 1, intPartLen[n, i - 1] + If[i > n, 0, intPartLen[n - i, i]]]; intPartLenPhi[n_] := intPartLen[n, EulerPhi[n]]; Table[intPartLenPhi[n], {n, 0, 99}] (* Jean-Fran├žois Alcover, Nov 11 2015, after Alois P. Heinz *)

PROG

(Haskell)

a227296 n = p [1 .. a000010 n] n where

   p _          0 = 1

   p []         _ = 0

   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

CROSSREFS

Cf. A079124, A057562.

Sequence in context: A245712 A285331 A237125 * A318846 A231263 A231451

Adjacent sequences:  A227293 A227294 A227295 * A227297 A227298 A227299

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 05 2013

STATUS

approved

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)