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 A379305 #5 Dec 27 2024 18:08:11
%S A379305 0,0,1,2,1,1,2,3,3,3,3,6,8,8,8,10,12,17,18,18,22,28,30,36,40,44,52,62,
%T A379305 67,78,87,97,113,129,137,156,177,200,227,251,271,312,350,382,425,475,
%U A379305 521,588,648,705,785,876,957,1061,1164,1272,1411,1558,1693,1866
%N A379305 Number of strict integer partitions of n with a unique prime part.
%e A379305 The a(2) = 1 through a(12) = 8 partitions (A=10, B=11):
%e A379305 (2) (3) (31) (5) (42) (7) (62) (54) (82) (B) (93)
%e A379305 (21) (51) (43) (71) (63) (541) (65) (A2)
%e A379305 (421) (431) (621) (631) (74) (B1)
%e A379305 (83) (642)
%e A379305 (92) (651)
%e A379305 (821) (741)
%e A379305 (831)
%e A379305 (921)
%t A379305 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Count[#,_?PrimeQ]==1&]],{n,0,30}]
%Y A379305 For all prime parts we have A000586, non-strict A000607 (ranks A076610).
%Y A379305 For no prime parts we have A096258, non-strict A002095 (ranks A320628).
%Y A379305 Ranked by A331915 /\ A005117 = squarefree positions of one in A257994.
%Y A379305 For a composite instead of prime we have A379303, non-strict A379302 (ranks A379301).
%Y A379305 The non-strict version is A379304.
%Y A379305 For squarefree instead of prime we have A379309, non-strict A379308 (ranks A379316).
%Y A379305 Considering 1 prime gives A379315, non-strict A379314 (ranks A379312).
%Y A379305 A000040 lists the prime numbers, differences A001223.
%Y A379305 A000041 counts integer partitions, strict A000009.
%Y A379305 A002808 lists the composite numbers, nonprimes A018252, differences A073783 or A065310.
%Y A379305 A095195 gives k-th differences of prime numbers.
%Y A379305 Cf. A000070, A023895, A034891, A036497, A038348, A204389, A302540, A320629, A330944.
%K A379305 nonn
%O A379305 0,4
%A A379305 _Gus Wiseman_, Dec 27 2024