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

%I A227296 #22 May 24 2018 09:25:34
%S A227296 1,1,1,2,3,6,4,14,15,26,23,55,34,100,90,146,186,296,199,489,434,725,
%T A227296 807,1254,919,1946,2063,2943,3036,4564,2462,6841,7665,9871,11098,
%U A227296 14744,12384,21636,23928,30677,31603,44582,31570,63260,69414,86420,99795,124753
%N A227296 Number of partitions of n into parts <= phi(n), where phi is Euler's totient function (cf. A000010).
%H A227296 Alois P. Heinz, <a href="/A227296/b227296.txt">Table of n, a(n) for n = 0..10000</a>
%F A227296 a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)*n). - _Vaclav Kotesovec_, May 24 2018
%p A227296 with(numtheory):
%p A227296 b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
%p A227296        b(n, i-1) +`if`(i>n, 0, b(n-i, i)))
%p A227296     end:
%p A227296 a:= n-> b(n, phi(n)):
%p A227296 seq(a(n), n=0..100);  # _Alois P. Heinz_, May 11 2015
%t A227296 (* Requires version 6.0+ *) Table[Length[IntegerPartitions[n, n, Range[EulerPhi[n]]]], {n, 0, 47}] (* _Ivan Neretin_, May 11 2015 *)
%t A227296 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_ *)
%o A227296 (Haskell)
%o A227296 a227296 n = p [1 .. a000010 n] n where
%o A227296    p _          0 = 1
%o A227296    p []         _ = 0
%o A227296    p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%Y A227296 Cf. A079124, A057562.
%K A227296 nonn
%O A227296 0,4
%A A227296 _Reinhard Zumkeller_, Jul 05 2013