A089653 Numbers k > 1 such that (product of prime factors of k) - 1 is a perfect square.

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

Offset: 1

Author

Joseph L. Pe, Jan 04 2004

Keywords

• nonn

Examples

			The prime factors of 10 are 2 and 5 and 2 * 5 - 1 = 9 is a square; so 10 belongs to the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007947, A089632. A091419 gives squares, A091420 gives square roots. Subsets: A002496, A003592 \ {1}.

Programs

Mathematica

ppf[n_] := Apply[Times, Transpose[FactorInteger[n]][[1]]]; Select[Range[2, 10^3], IntegerQ[Sqrt[ppf[ # ] - 1]] &]

PARI

isok(k) = (k>1) && issquare(vecprod(factor(k)[, 1])-1); \\ Michel Marcus, Sep 05 2023

Extensions

Name clarified by Michel Marcus, Sep 05 2023