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 A073630 Numbers k such that k*(prime(k) - 1) is a square. 0
 1, 2, 8, 1849, 22912, 40328, 646912, 3607298, 6323422, 7520900, 8962893, 23879700, 38043325, 157944268, 1105942626, 3604734726, 5239828426, 8179002096, 8179002106, 37234260225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Next term is > 2.5*10^10. - Ryan Propper, Nov 10 2006 a(21) > pi(10^12). - Donovan Johnson, Feb 26 2010 LINKS Table of n, a(n) for n=1..20. EXAMPLE 7520900*(prime(7520900) - 1) = 997787845328400 = 31587780^2 is a perfect square, so 7520900 is in the sequence. MATHEMATICA Do[k = n*Prime[n] - n; If[IntegerQ[Sqrt[k]], Print[n]], {n, 1, 670000000}] (* Ryan Propper, Aug 24 2005 *) PROG (PARI) isok(k) = issquare(k*(prime(k)-1)); \\ Michel Marcus, Feb 15 2021 CROSSREFS Sequence in context: A121015 A216619 A306241 * A027733 A054874 A174736 Adjacent sequences: A073627 A073628 A073629 * A073631 A073632 A073633 KEYWORD nonn,hard,more AUTHOR Benoit Cloitre, Aug 29 2002 EXTENSIONS More terms from Ryan Propper, Aug 24 2005 More terms from Ryan Propper, Nov 10 2006 a(20) from Donovan Johnson, Feb 26 2010 STATUS approved

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Last modified June 15 13:08 EDT 2024. Contains 373407 sequences. (Running on oeis4.)