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 A372889 #13 May 31 2024 10:04:56
%S A372889 1,2,3,7,15,31,62,127,255,511,1023,2047,4094,8191,16383,32767,65535,
%T A372889 131071,262142,524287,1048574,2097149,4194303,8388607,16777214,
%U A372889 33554431,67108863,134217727,268435455,536870911,1073741822,2147483647,4294967295,8589934591
%N A372889 Greatest squarefree number <= 2^n.
%F A372889 a(n) = A005117(A143658(n)).
%F A372889 a(n) = A070321(2^n). - _R. J. Mathar_, May 31 2024
%e A372889 The terms together with their binary expansions and binary indices begin:
%e A372889 1: 1 ~ {1}
%e A372889 2: 10 ~ {2}
%e A372889 3: 11 ~ {1,2}
%e A372889 7: 111 ~ {1,2,3}
%e A372889 15: 1111 ~ {1,2,3,4}
%e A372889 31: 11111 ~ {1,2,3,4,5}
%e A372889 62: 111110 ~ {2,3,4,5,6}
%e A372889 127: 1111111 ~ {1,2,3,4,5,6,7}
%e A372889 255: 11111111 ~ {1,2,3,4,5,6,7,8}
%e A372889 511: 111111111 ~ {1,2,3,4,5,6,7,8,9}
%e A372889 1023: 1111111111 ~ {1,2,3,4,5,6,7,8,9,10}
%e A372889 2047: 11111111111 ~ {1,2,3,4,5,6,7,8,9,10,11}
%e A372889 4094: 111111111110 ~ {2,3,4,5,6,7,8,9,10,11,12}
%e A372889 8191: 1111111111111 ~ {1,2,3,4,5,6,7,8,9,10,11,12,13}
%e A372889 16383: 11111111111111 ~ {1,2,3,4,5,6,7,8,9,10,11,12,13,14}
%e A372889 32767: 111111111111111 ~ {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
%t A372889 Table[NestWhile[#-1&,2^n,!SquareFreeQ[#]&],{n,0,15}]
%o A372889 (PARI) a(n) = my(k=2^n); while (!issquarefree(k), k--); k; \\ _Michel Marcus_, May 29 2024
%Y A372889 Positions of these terms in A005117 are A143658.
%Y A372889 For prime instead of squarefree we have A014234, delta A013603.
%Y A372889 For primes instead of powers of two we have A112925, opposite A112926.
%Y A372889 Least squarefree number >= 2^n is A372683, delta A373125, indices A372540.
%Y A372889 The opposite for prime instead of squarefree is A372684, firsts of A035100.
%Y A372889 The delta (difference from 2^n) is A373126.
%Y A372889 A000120 counts ones in binary expansion (binary weight), zeros A080791.
%Y A372889 A005117 lists squarefree numbers, first differences A076259.
%Y A372889 A030190 gives binary expansion, reversed A030308, length A070939 or A029837.
%Y A372889 A061398 counts squarefree numbers between primes, exclusive.
%Y A372889 A077643 counts squarefree terms between powers of 2, run-lengths of A372475.
%Y A372889 Cf. A029931, A048793, A049093, A049094, A077641, A372433, A372472, A372473, A372541, A373197, A373198.
%K A372889 nonn
%O A372889 0,2
%A A372889 _Gus Wiseman_, May 27 2024