%I #12 May 31 2024 09:20:52

%S 0,0,1,2,1,1,1,1,1,2,3,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,2,1,1,2,

%T 1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,2,3,1,1,1,2,1,2,1,1,1,1,1,2,1,1,1,1,

%U 2,3,3,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,1

%N Difference between 2^n and the least squarefree number >= 2^n.

%F a(n) = A372683(n)-2^n. - _R. J. Mathar_, May 31 2024

%t Table[NestWhile[#+1&,2^n,!SquareFreeQ[#]&]-2^n,{n,0,100}]

%Y For prime instead of squarefree we have A092131, opposite A013603.

%Y For primes instead of powers of 2: A240474, A240473, A112926, A112925.

%Y Difference between 2^n and A372683(n).

%Y The opposite is A373126, delta of A372889.

%Y A005117 lists squarefree numbers, first differences A076259.

%Y A053797 gives lengths of gaps between squarefree numbers.

%Y A061398 counts squarefree numbers between primes (exclusive).

%Y A070939 or (preferably) A029837 gives length of binary expansion.

%Y A077643 counts squarefree terms between powers of 2, run-lengths of A372475.

%Y A143658 counts squarefree numbers up to 2^n.

%Y Cf. A372473 (firsts of A372472), A372541 (firsts of A372433).

%Y For primes between powers of 2:

%Y - sum A293697 (except initial terms)

%Y - length A036378

%Y - min A104080 or A014210, indices A372684 (firsts of A035100)

%Y - max A014234, delta A013603

%Y Cf. A010036, A029931, A049093-A049096, A077641, A372540, A373197, A373198.

%K nonn

%O 0,4

%A _Gus Wiseman_, May 28 2024