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 A245569 Numbers n such that binomial(2^n-1,n) is squarefree. 1
 0, 1, 2, 3, 4, 6, 11, 12, 21, 28, 29, 31, 51, 54, 55, 57 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Motivated by the previously existing entry for the subsequence A246699 of squarefree terms in this sequence. Conjectured to be finite. Next term, if it exists, is larger than 500. LINKS MATHEMATICA Select[Range[0, 57], SquareFreeQ[Binomial[2^#-1, #]]&] (* Ivan N. Ianakiev, Nov 18 2014 *) PROG (PARI) is(n)=issquarefree(binomial(2^n-1, n)) (PARI) is(n)={t=1; n&&n=vecsort(concat(vector(n, k, factor(if(kx)(t=(2^n-k)/k/denominator(t)), 0)~))); for(i=2, #n, if(n[1, i]==n[1, i-1], n[2, i]+=n[2, i-1]; n[2, i-1]=0)); !n||vecmax(n[2, ])<2} \\ Limiting "factor" to precomputed primes might yield a false positive, but no term > 57 is found so far. CROSSREFS Cf. A000225, A005117, A136556. Sequence in context: A029457 A014859 A084166 * A018297 A050886 A341652 Adjacent sequences:  A245566 A245567 A245568 * A245570 A245571 A245572 KEYWORD nonn,more AUTHOR M. F. Hasler, Nov 17 2014 STATUS approved

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Last modified September 27 03:01 EDT 2022. Contains 357051 sequences. (Running on oeis4.)