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 A379303 #6 Dec 26 2024 23:03:08
%S A379303 0,0,0,0,1,1,2,3,3,6,6,8,10,10,13,15,17,20,22,24,28,31,36,40,44,50,55,
%T A379303 62,70,75,83,89,97,108,115,128,136,146,161,172,188,203,215,233,249,
%U A379303 269,291,309,331,353,376,405,433,459,490,518,554,592,629,670,705
%N A379303 Number of strict integer partitions of n with a unique composite part.
%e A379303 The a(4) = 1 through a(11) = 8 partitions:
%e A379303 (4) (4,1) (6) (4,3) (8) (9) (10) (6,5)
%e A379303 (4,2) (6,1) (6,2) (5,4) (8,2) (7,4)
%e A379303 (4,2,1) (4,3,1) (6,3) (9,1) (8,3)
%e A379303 (8,1) (5,4,1) (9,2)
%e A379303 (4,3,2) (6,3,1) (10,1)
%e A379303 (6,2,1) (4,3,2,1) (5,4,2)
%e A379303 (6,3,2)
%e A379303 (8,2,1)
%t A379303 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Count[#,_?CompositeQ]==1&]],{n,0,30}]
%Y A379303 If no parts are composite we have A036497, non-strict A034891 (ranks A302540).
%Y A379303 If all parts are composite we have A204389, non-strict A023895 (ranks A320629).
%Y A379303 The non-strict version is A379302, ranks A379301 (positions of 1 in A379300).
%Y A379303 For a unique prime we have A379305, non-strict A379304 (ranks A331915).
%Y A379303 A000040 lists the prime numbers, differences A001223.
%Y A379303 A000041 counts integer partitions, strict A000009.
%Y A379303 A002808 lists the composite numbers, nonprimes A018252.
%Y A379303 A066247 is the characteristic function for the composite numbers.
%Y A379303 A377033 gives k-th differences of composite numbers, see A073445, A377034-A377037.
%Y A379303 Cf. A000070, A000586, A000607, A002095, A038348, A096258, A113646, A376680, A379308, A379309, A379314, A379315.
%K A379303 nonn
%O A379303 0,7
%A A379303 _Gus Wiseman_, Dec 25 2024