A377431 Numbers k such that there is at least one squarefree number between prime(k)+1 and prime(k+1)-1.

3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 42, 44, 46, 47, 48, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84, 85, 86

Offset: 1

Author

Gus Wiseman, Oct 29 2024

Keywords

• nonn

Examples

			Primes 4 and 5 are 7 and 11, and the interval (8,9,10) contains 10, which is squarefree, so 4 is in the sequence.
		

Crossrefs

These are the positive positions in A061398, or terms >= 2 in A373198.

The complement (no squarefree numbers) is A068360.

For prime-power instead of squarefree we have A377057, strict version A377287.

For exactly one squarefree number we have A377430.

A000040 lists the primes, differences A001223, seconds A036263.

A002808 lists the composites, complement A008578.

A005117 lists the squarefree numbers, complement A013929.

A377038 gives k-differences of squarefree numbers.

Cf. A007674, A013603, A029707, A036378, A046933, A072284, A076259, A077641, A077643, A075526, A078147, A112925, A112926, A120992, A293697.

Programs

Mathematica

Select[Range[100], Length[Select[Range[Prime[#]+1,Prime[#+1]-1],SquareFreeQ]]>=1&]