This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A089632 #17 Apr 15 2019 03:23:57 %S A089632 3,9,15,27,35,45,75,81,135,143,175,195,225,243,245,255,323,375,399, %T A089632 405,483,585,675,729,765,875,899,975,1023,1125,1155,1197,1215,1225, %U A089632 1275,1295,1443,1449,1573,1599,1715,1755,1763,1859,1875,2025,2187,2295,2535 %N A089632 1 + product of prime factors of n is a perfect square. %C A089632 From _Robert Israel_, Apr 14 2019: (Start) %C A089632 Numbers k such that A076618(k) is a square. %C A089632 All terms are odd. %C A089632 Squarefree terms are k^2-1 for k in A067874. %C A089632 (End) %H A089632 Robert Israel, <a href="/A089632/b089632.txt">Table of n, a(n) for n = 1..10000</a> %e A089632 The prime factors of 35 are 5 and 7 and 5 * 7 + 1 = 36 is a square; so 35 belongs to the sequence. %p A089632 filter:= n -> issqr(1+convert(numtheory:-factorset(n),`*`)): %p A089632 select(filter, [$1..10000]); # _Robert Israel_, Apr 14 2019 %t A089632 ppf[n_] := Apply[Times, Transpose[FactorInteger[n]][[1]]]; Select[Range[2, 10^3], IntegerQ[Sqrt[ppf[ # ] + 1]] &] %o A089632 (PARI) isok(n) = my(f=factor(n)); issquare(1+prod(k=1, #f~, f[k,1])); \\ _Michel Marcus_, Apr 15 2019 %Y A089632 Cf. A089653. A091278 gives squares, A091279 gives square roots. %Y A089632 Cf. A067874, A076618. %K A089632 nonn %O A089632 1,1 %A A089632 _Joseph L. Pe_, Jan 04 2004 %E A089632 More terms from _Ray Chandler_, Jan 05 2004