cp's OEIS Frontend

A319913 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.

%I A319913 #15 Jun 03 2019 00:36:44
%S A319913 1,2,3,5,7,16,20,37,53,81,107,177,227,332,449,647,830,1162,1480,2032,
%T A319913 2597,3447,4348,5775,7251,9374,11758,15026,18640,23688,29220,36771,
%U A319913 45128,56168,68674,85015,103394,126923,153871,187911,226653
%N A319913 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 A319913 All parts of the integer partition must be used in such a combination.
%H A319913 Charlie Neder, <a href="/A319913/b319913.txt">Table of n, a(n) for n = 1..46</a>
%F A319913 a(n) >= A000041(n).
%F A319913 a(n) >= A001055(n).
%e A319913 The a(7) = 20 partitions (which are not all partitions of 7):
%e A319913   (7),
%e A319913   (61), (52), (43),
%e A319913   (511), (321), (421), (331), (322),
%e A319913   (3111), (4111), (2211), (3211), (2221),
%e A319913   (21111), (31111), (22111),
%e A319913   (111111), (211111),
%e A319913   (1111111).
%e A319913 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 A319913 Cf. A000792, A001970, A005520, A048249, A066739, A066815, A275870, A319850, A318949, A319909, A319910, A319912, A319925.
%K A319913 nonn
%O A319913 1,2
%A A319913 _Gus Wiseman_, Oct 01 2018
%E A319913 a(13)-a(41) from _Charlie Neder_, Jun 02 2019