cp's OEIS Frontend

A373126 Difference between 2^n and the greatest squarefree number <= 2^n.

%I A373126 #11 May 31 2024 09:22:09
%S A373126 0,0,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,2,3,1,1,2,1,1,1,1,1,2,1,1,1,
%T A373126 1,1,2,1,1,1,2,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,2,1,1,2,1,
%U A373126 1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,2,1,1
%N A373126 Difference between 2^n and the greatest squarefree number <= 2^n.
%F A373126 a(n) = 2^n-A372889(n). - _R. J. Mathar_, May 31 2024
%e A373126 The greatest squarefree number <= 2^21 is 2097149, and 2^21 = 2097152, so a(21) = 3.
%t A373126 Table[2^n-NestWhile[#-1&,2^n,!SquareFreeQ[#]&],{n,0,100}]
%Y A373126 For prime instead of squarefree we have A013603, opposite A092131.
%Y A373126 For primes instead of powers of 2: A240474, A240473, A112926, A112925.
%Y A373126 Difference between 2^n and A372889.
%Y A373126 The opposite is A373125, delta of A372683.
%Y A373126 A005117 lists squarefree numbers, first differences A076259.
%Y A373126 A053797 gives lengths of gaps between squarefree numbers.
%Y A373126 A061398 counts squarefree numbers between primes (exclusive).
%Y A373126 A070939 or (preferably) A029837 gives length of binary expansion.
%Y A373126 A077643 counts squarefree terms between powers of 2, run-lengths of A372475.
%Y A373126 A143658 counts squarefree numbers up to 2^n.
%Y A373126 Cf. A372473 (firsts of A372472), A372541 (firsts of A372433).
%Y A373126 For primes between powers of 2:
%Y A373126 - sum A293697 (except initial terms)
%Y A373126 - length A036378
%Y A373126 - min A104080 or A014210, indices A372684 (firsts of A035100)
%Y A373126 - max A014234
%Y A373126 Cf. A010036, A029931, A046933, A049093-A049096, A077641, A372540, A373197.
%K A373126 nonn
%O A373126 0,7
%A A373126 _Gus Wiseman_, May 29 2024