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 A089653 Numbers k > 1 such that (product of prime factors of k) - 1 is a perfect square. 5
 2, 4, 5, 8, 10, 16, 17, 20, 25, 26, 32, 37, 40, 50, 52, 64, 65, 80, 82, 100, 101, 104, 122, 125, 128, 145, 160, 164, 170, 197, 200, 208, 226, 244, 250, 256, 257, 289, 290, 320, 325, 328, 338, 340, 362, 400, 401, 416, 442, 452, 485, 488, 500, 512, 530, 577, 580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE The prime factors of 10 are 2 and 5 and 2 * 5 - 1 = 9 is a square; so 10 belongs to the sequence. MATHEMATICA ppf[n_] := Apply[Times, Transpose[FactorInteger[n]][[1]]]; Select[Range[2, 10^3], IntegerQ[Sqrt[ppf[ # ] - 1]] &] PROG (PARI) isok(k) = (k>1) && issquare(vecprod(factor(k)[, 1])-1); \\ Michel Marcus, Sep 05 2023 CROSSREFS Cf. A007947, A089632. A091419 gives squares, A091420 gives square roots. Subsets: A002496, A003592 \ {1}. Sequence in context: A199799 A032937 A126684 * A180252 A191203 A216686 Adjacent sequences: A089650 A089651 A089652 * A089654 A089655 A089656 KEYWORD nonn AUTHOR Joseph L. Pe, Jan 04 2004 EXTENSIONS Name clarified by Michel Marcus, Sep 05 2023 STATUS approved

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Last modified December 2 09:50 EST 2023. Contains 367517 sequences. (Running on oeis4.)