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 A373643 #21 Dec 03 2024 11:45:20
%S A373643 0,0,0,0,1,0,1,1,2,0,1,1,0,2,3,2,1,1,1,1,2,1,2,3,3,0,1,1,1,5,0,3,0,4,
%T A373643 1,3,2,1,3,2,1,3,1,1,1,4,3,2,1,1,2,1,5,1,2,2,1,3,2,0,3,6,1,1,2,4,3,4,
%U A373643 1,3,1,3,3,3,1,3,2,1,3,3,1,4,1,1,2,2,3
%N A373643 Number of k between consecutive primes such that k is neither squarefree nor prime powers.
%H A373643 Michael De Vlieger, <a href="/A373643/b373643.txt">Table of n, a(n) for n = 1..10000</a>
%F A373643 a(n) = A001223(n) - A061398(n) - A080101(n) - 1.
%e A373643 Let S = A126706, the sequence of k neither squarefree nor prime powers.
%e A373643 a(1..4) = 0 since S(1) = 12.
%e A373643 a(5) = 1 since (11, 12, 13) contains S(1) = 12.
%e A373643 a(6) = 0 since (13, 14, 15, 16, 17) contains no number in S.
%e A373643 a(7) = 1 since (17, 18, 19) contains S(2) = 18.
%e A373643 a(8) = 1 since (19, 20, 21, 22, 23) contains S(3) = 20.
%e A373643 a(9) = 2 since (23, 24, 25, 26, 27, 28, 29) contains S(4) = 24 and S(5) = 28, etc.
%t A373643 Table[Count[Range[Prime[i] + 1, Prime[i + 1] - 1], _?(Nor[SquareFreeQ[#], PrimePowerQ[#]] &)], {i, 120}]
%Y A373643 Cf. A001223, A061398, A080101, A126706.
%K A373643 nonn,easy
%O A373643 1,9
%A A373643 _Michael De Vlieger_, Dec 03 2024