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%I #26 Sep 05 2023 18:25:51
%S 2,4,5,8,10,16,17,20,25,26,32,37,40,50,52,64,65,80,82,100,101,104,122,
%T 125,128,145,160,164,170,197,200,208,226,244,250,256,257,289,290,320,
%U 325,328,338,340,362,400,401,416,442,452,485,488,500,512,530,577,580
%N Numbers k > 1 such that (product of prime factors of k) - 1 is a perfect square.
%H Amiram Eldar, <a href="/A089653/b089653.txt">Table of n, a(n) for n = 1..10000</a>
%e The prime factors of 10 are 2 and 5 and 2 * 5 - 1 = 9 is a square; so 10 belongs to the sequence.
%t ppf[n_] := Apply[Times, Transpose[FactorInteger[n]][[1]]]; Select[Range[2, 10^3], IntegerQ[Sqrt[ppf[ # ] - 1]] &]
%o (PARI) isok(k) = (k>1) && issquare(vecprod(factor(k)[, 1])-1); \\ _Michel Marcus_, Sep 05 2023
%Y Cf. A007947, A089632. A091419 gives squares, A091420 gives square roots. Subsets: A002496, A003592 \ {1}.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Jan 04 2004
%E Name clarified by _Michel Marcus_, Sep 05 2023
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