%I #15 Jun 03 2019 00:36:44

%S 1,2,3,5,7,16,20,37,53,81,107,177,227,332,449,647,830,1162,1480,2032,

%T 2597,3447,4348,5775,7251,9374,11758,15026,18640,23688,29220,36771,

%U 45128,56168,68674,85015,103394,126923,153871,187911,226653

%N Number of distinct integer partitions whose parts can be combined together using additions and multiplications to obtain n, with the exception that 1's can only be added and not multiplied with other parts.

%C All parts of the integer partition must be used in such a combination.

%H Charlie Neder, <a href="/A319913/b319913.txt">Table of n, a(n) for n = 1..46</a>

%F a(n) >= A000041(n).

%F a(n) >= A001055(n).

%e The a(7) = 20 partitions (which are not all partitions of 7):

%e (7),

%e (61), (52), (43),

%e (511), (321), (421), (331), (322),

%e (3111), (4111), (2211), (3211), (2221),

%e (21111), (31111), (22111),

%e (111111), (211111),

%e (1111111).

%e This list contains (2211) because we can write 7 = (2+1)*2+1. It contains (321) because we can write 7 = 3*2+1, even though the sum of parts is only 6.

%Y Cf. A000792, A001970, A005520, A048249, A066739, A066815, A275870, A319850, A318949, A319909, A319910, A319912, A319925.

%K nonn

%O 1,2

%A _Gus Wiseman_, Oct 01 2018

%E a(13)-a(41) from _Charlie Neder_, Jun 02 2019