This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379302 #10 Dec 26 2024 23:02:52
%S A379302 0,0,0,0,1,1,3,4,7,11,16,23,32,43,58,77,100,129,164,207,259,323,398,
%T A379302 489,595,723,872,1049,1255,1495,1774,2097,2472,2903,3399,3969,4618,
%U A379302 5362,6210,7173,8268,9506,10907,12488,14271,16278,18532,21061,23893,27064
%N A379302 Number of integer partitions of n with a unique composite part.
%e A379302 The a(0) = 0 through a(9) = 11 partitions:
%e A379302 . . . . (4) (41) (6) (43) (8) (9)
%e A379302 (42) (61) (62) (54)
%e A379302 (411) (421) (422) (63)
%e A379302 (4111) (431) (81)
%e A379302 (611) (432)
%e A379302 (4211) (621)
%e A379302 (41111) (4221)
%e A379302 (4311)
%e A379302 (6111)
%e A379302 (42111)
%e A379302 (411111)
%t A379302 Table[Length[Select[IntegerPartitions[n],Count[#,_?CompositeQ]==1&]],{n,0,30}]
%Y A379302 If all parts are composite we have A023895 (strict A204389), ranks A320629.
%Y A379302 If no parts are composite we have A034891 (strict A036497), ranks A302540.
%Y A379302 Ranked by A379301 = positions of 1 in A379300.
%Y A379302 The strict case is A379303.
%Y A379302 For a unique prime part we have A379304 (strict A379305), ranks A331915.
%Y A379302 A000041 counts integer partitions, strict A000009.
%Y A379302 A002808 lists the composite numbers, nonprimes A018252.
%Y A379302 A066247 is the characteristic function for the composite numbers.
%Y A379302 A377033 gives k-th differences of composite numbers.
%Y A379302 Cf. A000070, A000586, A000607, A002095, A038348, A096258, A114374, A330944, A379308, A379309, A379314, A379315.
%K A379302 nonn
%O A379302 0,7
%A A379302 _Gus Wiseman_, Dec 25 2024