A050675 Numbers n such that concatenation of numbers from 1 to n is nonsquarefree.
2, 6, 8, 9, 12, 16, 17, 18, 20, 24, 25, 26, 27, 28, 32, 35, 36, 40, 44, 45, 48, 50, 52, 53, 54, 56, 60, 62, 63, 64, 68, 71, 72, 75, 76, 80, 81, 84, 85, 88, 89, 90, 92, 96, 98, 99, 100, 104, 107, 108, 112, 116, 117
Offset: 1
Examples
6 is a term because 123456 = 2*2*2*2*2*2*3*643 = 2^6*3*643, not squarefree.
Links
- Patrick De Geest, Normal Smarandache Concatenated Numbers, Prime factors from 1 up to n
- M. Fleuren, Factors and primes of Smarandache sequences.
- M. Fleuren, Smarandache Factors and Reverse factors
- Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles & Problems Connection.
Programs
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Magma
a:=[];c:=1; for n in [2..55] do c:=c*10^#Intseq(n)+n; if not IsSquarefree(c) then Append(~a,n); end if; end for; a; // Marius A. Burtea, Oct 15 2019
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Mathematica
t={}; m=1; Do[m=FromDigits[Flatten[IntegerDigits[{m,n}]]]; If[!SquareFreeQ[m],AppendTo[t,n]],{n,2,32}]; t (* Jayanta Basu, May 30 2013 *) Module[{nn=120,cct},cct=Table[If[SquareFreeQ[FromDigits[Flatten[IntegerDigits/@Range[ n]]]],0,1],{n,nn}];Position[cct,?(#==1&)]]//Flatten (* _Harvey P. Dale, Sep 20 2023 *) -
PARI
conc(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s); \\ A007908 isok(n) = ! issquarefree(conc(n)); \\ Michel Marcus, Oct 16 2019
Formula
n < a(n) < 2.4n for n > 10. The upper constant can be lowered to 25/11 with more work. - Charles R Greathouse IV, Sep 20 2012
Extensions
Corrected by Charles R Greathouse IV, Sep 20 2012
More terms from Sean A. Irvine, Aug 16 2021
Comments