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%I #14 May 25 2013 08:16:22
%S 2,6,6,687,1386,82305020
%N Least i > 1 such that the sum of the digits in the base-j representation of i is invariant over all j in the first n squarefree numbers.
%e For n = 4 the number 687 is the least i > 1 such that s_2 (i) = s_3 (i) = s_5 (i) = s_6 (i), where s_k (i) is the sum of the digits in the base-k representation of i.
%o (PARI) tsqf(n) = {sqfs = vector(n); ipos = 1; na = 2; while (ipos <= n, if (issquarefree(na), sqfs[ipos] = na; ipos++;); na++;); return (sqfs);}
%o iok(i, sqfs) = {vdig = digits(i, sqfs[1]); sdig = sum(k=1, #vdig, vdig[k]); for (j=2, #sqfs, vdig = digits(i, sqfs[j]); if (sum(k=1, #vdig, vdig[k]) != sdig, return(0));); return (1);}
%o a(n) = {sqfs = tsqf(n); ok = 0; i = 2; while(! ok, if (iok(i, sqfs), ok = 1, i++);); return (i);} \\ _Michel Marcus_, May 25 2013
%Y Cf. A005117 (squarefree numbers).
%K nonn,base
%O 1,1
%A _Jeffrey Shallit_, Nov 14 2012
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