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 A140746 Numbers n such that n^2 + 3 is powerful, (i.e., is of the form a^2*b^3, with a>=1, b>=1). 1
 1, 37, 79196, 177833, 5290738, 9667939010 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Florian Luca proved that this sequence is infinite, by showing that 37*x(7*k) + 98*y(7*k) is in the sequence, where x(k) = A001081(k) and y(k) = A001080(k) are solutions of the Pell equation x^2 - 7*y^2 = 1. The sequence of these numbers is 37, 9667939010, 2524807950507510523, 659360302164952911361460078, ... - Amiram Eldar, Aug 22 2018 a(7) <= 457189690981. - Giovanni Resta, Aug 23 2018 REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 37, pp 14, Ellipses, Paris 2008. LINKS EXAMPLE 37 is the sequence since 37^2 + 3 = 1372 = 2^2 * 7^3 is powerful. MATHEMATICA powerfulQ[n_] := Min@FactorInteger[n][[All, 2]] > 1; Select[Range, powerfulQ[#^2 + 3] &] (* Amiram Eldar, Aug 22 2018 *) PROG (PARI) isok(n) = vecmin(factor(n^2+3)[, 2]) > 1; \\ Michel Marcus, Aug 24 2018 CROSSREFS Cf. A001694 (powerful), A001080, A001081, A117950 (n^2+3). Sequence in context: A015061 A015037 A262786 * A262646 A063681 A289820 Adjacent sequences:  A140743 A140744 A140745 * A140747 A140748 A140749 KEYWORD nonn,more AUTHOR Lekraj Beedassy, Jul 12 2008 EXTENSIONS a(5) corrected and a(6) removed by Amiram Eldar, Aug 22 2018 a(6) from Giovanni Resta, Aug 23 2018 STATUS approved

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Last modified September 23 16:41 EDT 2020. Contains 337315 sequences. (Running on oeis4.)