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 A379308 #7 Dec 27 2024 08:44:36
%S A379308 0,1,1,1,0,2,2,2,0,3,5,5,1,6,9,9,2,10,14,18,6,18,24,30,11,28,39,47,24,
%T A379308 48,63,76,41,74,95,118,65,120,149,181,107,181,221,266,169,266,335,398,
%U A379308 262,394,487,578,391,578,697,844,592,834,997,1198,867
%N A379308 Number of integer partitions of n with a unique squarefree part.
%e A379308 The a(1) = 1 through a(11) = 5 partitions:
%e A379308 (1) (2) (3) . (5) (6) (7) . (5,4) (10) (11)
%e A379308 (4,1) (4,2) (4,3) (8,1) (6,4) (7,4)
%e A379308 (4,4,1) (8,2) (8,3)
%e A379308 (9,1) (9,2)
%e A379308 (4,4,2) (4,4,3)
%t A379308 Table[Length[Select[IntegerPartitions[n],Count[#,_?SquareFreeQ]==1&]],{n,0,30}]
%Y A379308 If all parts are squarefree we have A073576 (strict A087188), ranks A302478.
%Y A379308 If no parts are squarefree we have A114374 (strict A256012), ranks A379307.
%Y A379308 For composite instead of squarefree we have A379302 (strict A379303), ranks A379301.
%Y A379308 For prime instead of squarefree we have A379304, (strict A379305), ranks A331915.
%Y A379308 The strict case is A379309.
%Y A379308 For old prime instead of squarefree we have A379314, (strict A379315), ranks A379312.
%Y A379308 Ranked by A379316, positions of 1 in A379306.
%Y A379308 A000041 counts integer partitions, strict A000009.
%Y A379308 A005117 lists the squarefree numbers, differences A076259.
%Y A379308 A013929 lists the nonsquarefree numbers, differences A078147.
%Y A379308 A377038 gives k-th differences of squarefree numbers.
%Y A379308 A379310 counts nonsquarefree prime indices.
%Y A379308 Cf. A000586, A000607, A002095, A013928, A023895, A034891, A072284, A073247, A120327, A175804, A376657, A377430.
%K A379308 nonn
%O A379308 0,6
%A A379308 _Gus Wiseman_, Dec 26 2024