A378458 Squarefree numbers k such that k + 1 is squarefree but k + 2 is not.

2, 6, 10, 14, 22, 30, 34, 38, 42, 46, 58, 61, 66, 70, 73, 78, 82, 86, 94, 102, 106, 110, 114, 118, 122, 130, 133, 138, 142, 145, 154, 158, 166, 173, 178, 182, 186, 190, 194, 202, 205, 210, 214, 218, 222, 226, 230, 238, 246, 254, 258, 262, 266, 273, 277, 282

Offset: 1

Author

Gus Wiseman, Dec 02 2024

Keywords

• nonn

Comments

These are the positions of 2 in A378369 (difference between n and the next nonsquarefree number).

The asymptotic density of this sequence is Product_{p prime} (1 - 2/p^2) - Product_{p prime} (1 - 3/p^2) = A065474 - A206256 = 0.19714711803343537224... . - Amiram Eldar, Dec 03 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A007675 within A007674.

The version for prime power instead of nonsquarefree is a subset of A006549.

Another variation is A073247.

The version for nonprime instead of squarefree is A179384.

Positions of 0 in A378369 are A013929.

Positions of 1 in A378369 are A373415.

Positions of 2 in A378369 are A378458 (this).

Positions of 3 in A378369 are A007675.

A000961 lists the powers of primes, differences A057820.

A120327 gives the least nonsquarefree number >= n.

A378373 counts composite numbers between nonsquarefree numbers.

Cf. A065474, A067535, A081221, A206256, A236575, A377046, A378033, A378039, A378086.

Programs

Mathematica

Select[Range[100],NestWhile[#+1&,#,SquareFreeQ[#]&]==#+2&]

PARI

list(lim) = my(q1 = 1, q2 = 1, q3); for(k = 3, lim, q3 = issquarefree(k); if(q1 && q2 &&!q3, print1(k-2, ", ")); q1 = q2; q2 = q3); \\ Amiram Eldar, Dec 03 2024