A227296 Number of partitions of n into parts <= phi(n), where phi is Euler's totient function (cf. A000010).

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

Offset: 0

Author

Reinhard Zumkeller, Jul 05 2013

Keywords

• nonn

Links

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

Crossrefs

Cf. A079124, A057562.

Programs

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

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-François Alcover, Nov 11 2015, after Alois P. Heinz *)

Formula

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