A077378 Squarefree numbers whose external as well as internal digits form a squarefree number.

123, 127, 129, 130, 131, 133, 134, 137, 139, 151, 154, 155, 157, 159, 161, 163, 165, 167, 170, 173, 174, 177, 179, 221, 222, 223, 226, 229, 231, 233, 239, 251, 253, 259, 262, 263, 266, 269, 271, 273, 321, 323, 327, 329, 330, 331, 334, 335, 337, 339, 353, 354, 355, 357, 358

Offset: 1

Author

Amarnath Murthy, Nov 06 2002

Keywords

• base
• easy
• nonn

Comments

Here 1 is treated as not squarefree. - Andrew Howroyd, Sep 19 2024

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A077376 and A077377.

Cf. A005117, A077379, A077380.

Programs

Mathematica

A077378Q[k_] := k >= 100 && SquareFreeQ[k] && SquareFreeQ[FromDigits[#[[{1, -1}]]]] && FromDigits[#[[2;; -2]]] > 1 && SquareFreeQ[FromDigits[#[[2;; -2]]]] & [IntegerDigits[k]];
Select[Range[500], A077378Q] (* Paolo Xausa, Feb 19 2025 *)

PARI

isok(k)={if(issquarefree(k) && k>=100, my(b=10^logint(k,10), m=k%b\10); m!=1 && issquarefree(m) && issquarefree(k\b*10+k%10), 0)} \\ Andrew Howroyd, Sep 19 2024

Extensions

Offset changed and a(29) onwards from Andrew Howroyd, Sep 19 2024