A112345 - OEIS

%I #12 Mar 22 2017 12:52:19

%S 1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,2,0,1,1,2,0,1,1,2,

%T 1,1,3,2,1,1,3,2,1,1,3,3,1,1,3,4,1,1,4,4,1,1,4,4,2,1,4,6,2,2,4,6,2,2,

%U 4,6,3,2,5,6,4,2,6,6,4,2,6,7,4,3,6,9,4,3,7,9,5,3,7,9,6,3,7,10,6,3,8,11,6,3,8

%N Number of partitions of n into distinct perfect powers.

%H Vaclav Kotesovec, <a href="/A112345/b112345.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Partition.html">Partition</a>

%F G.f.: Product_{k>=2} (1 + x^A001597(k)). - _Ilya Gutkovskiy_, Mar 21 2017

%e a(40) = #{36+4, 32+8, 27+9+4} = 3.

%Y Cf. A001597, A000009, A033461, A039966, A112344, A284171.

%K nonn

%O 0,26

%A _Reinhard Zumkeller_, Sep 05 2005

%E a(0)=1 prepended by _Ilya Gutkovskiy_, Mar 21 2017