A077378 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

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 *)

PROG

(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

CROSSREFS

Intersection of A077376 and A077377.

Cf. A005117, A077379, A077380.

Sequence in context: A308004 A192231 A341992 * A031509 A351479 A247616

Adjacent sequences: A077375 A077376 A077377 * A077379 A077380 A077381

KEYWORD

base,easy,nonn,changed

AUTHOR

Amarnath Murthy, Nov 06 2002

EXTENSIONS

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

STATUS

approved