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

1,1

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