A373125 - OEIS

A373125

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

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, 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, 2, 3, 3, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..86.

FORMULA

a(n) = A372683(n)-2^n. - R. J. Mathar, May 31 2024

MATHEMATICA

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

CROSSREFS

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

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

Difference between 2^n and A372683(n).

The opposite is A373126, delta of A372889.

A005117 lists squarefree numbers, first differences A076259.

A053797 gives lengths of gaps between squarefree numbers.

A061398 counts squarefree numbers between primes (exclusive).

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

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

A143658 counts squarefree numbers up to 2^n.

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

For primes between powers of 2:

- sum A293697 (except initial terms)

- length A036378

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

- max A014234, delta A013603

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

Sequence in context: A326753 A062093 A177457 * A357139 A046214 A232088

Adjacent sequences: A373122 A373123 A373124 * A373126 A373127 A373128

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 28 2024

STATUS

approved