A091420 -id:A091420 - cp's OEIS frontend

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

Joseph L. Pe, Jan 04 2004

nonn

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

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

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

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

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

Name clarified by Michel Marcus, Sep 05 2023

A091419 Squares arising in A089653.

Original entry on oeis.org

1, 1, 4, 1, 9, 1, 16, 9, 4, 25, 1, 36, 9, 9, 25, 1, 64, 9, 81, 9, 100, 25, 121, 4, 1, 144, 9, 81, 169, 196, 9, 25, 225, 121, 9, 1, 256, 16, 289, 9, 64, 81, 25, 169, 361, 9, 400, 25, 441, 225, 484, 121, 9, 1, 529, 576, 289, 4, 625, 9, 81, 25, 676, 169, 361, 144, 729, 784, 9

Offset: 1

Ray Chandler, Jan 05 2004

nonn

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

A091420 gives square roots.

Cf. A007947.

a(n) = A007947(A089653(n)) - 1. - Amiram Eldar, Sep 29 2019

cp's OEIS Frontend

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

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