A076786 Squarefree numbers such that in decimal representation all their prefixes are also squarefree.

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119, 130, 131, 133, 134, 137

Offset: 1

Author

Reinhard Zumkeller, Nov 16 2002

Keywords

• nonn
• base

Comments

m is a term iff A008966(floor(m/10^k))=1 for 0<=k<=A004216(n);

a(n)=A005117(n) for n<=26, but A005117(27)=41 is not a term, as 4=2^2 is not squarefree.

Examples

			143=11*13 is a term, as also 14=2*7 and 1 are squarefree.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Select[Range[200],AllTrue[FromDigits/@Table[Take[IntegerDigits[#],{1,n}],{n,IntegerLength[#]}],SquareFreeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 23 2020 *)