A386527 Numbers k in A055932 such that both k-1 and k+1 are not squarefree.

291600, 1406250, 2097152, 13436928, 34012224, 36382500, 46656000, 180033840, 393216000, 1073741824, 1360800000, 1771470000, 4900921200, 8576868300, 12884901888, 13588459500, 13608154560, 17496198720, 46490458680, 113810780160, 125475189840, 141557760000, 181474110720

Offset: 1

Author

Michael De Vlieger, Jul 24 2025

Keywords

• nonn

Comments

Superset of A386526.

Examples

			Table of n, a(n), showing exponents of prime factors of a(n), and the prime decomposition of a(n)-1 and a(n)+1 for n = 1..6:
                Exponents
n       a(n)    2.3.5.7.11  a(n)-1                a(n)+1
----------------------------------------------------------------------
1     291600    4.6.2       7^2 * 11 * 541        17^2 * 1009
2    1406250    1.2.7      13^2 * 53 * 157        7^2 * 11 * 2609
3    2097152   21           7^2 * 127 * 337       3^2 * 43 * 5419
4   13436928   11.8         7^2 * 274223         11^2 * 111049
5   34012224    6.12        7^3 * 17 * 19 * 307   5^2 * 13 * 229 * 457
6   36382500    2.3.4.2.1  17^2 * 31^2 * 131     29^2 * 43261
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..508 (all terms less than A002110(16)).
• Michael De Vlieger, Mathematica algorithm for A055932.

Crossrefs

Cf. A000079, A002110, A013929, A025487, A055932, A384530, A386526.

Programs

Mathematica

(* Load the Mathematica algorithm in Links, then: *)
Select[Union@ Flatten[a055932[10]], AllTrue[# + {-1, 1}, Not @* SquareFreeQ] &]