A076786 - OEIS

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

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

OFFSET

1,2

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.

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Sequence in context: A005117 A144338 A077377 * A298540 A326535 A358977

Adjacent sequences: A076783 A076784 A076785 * A076787 A076788 A076789

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Nov 16 2002

STATUS

approved