A089632 - OEIS

%I #17 Apr 15 2019 03:23:57

%S 3,9,15,27,35,45,75,81,135,143,175,195,225,243,245,255,323,375,399,

%T 405,483,585,675,729,765,875,899,975,1023,1125,1155,1197,1215,1225,

%U 1275,1295,1443,1449,1573,1599,1715,1755,1763,1859,1875,2025,2187,2295,2535

%N 1 + product of prime factors of n is a perfect square.

%C From _Robert Israel_, Apr 14 2019: (Start)

%C Numbers k such that A076618(k) is a square.

%C All terms are odd.

%C Squarefree terms are k^2-1 for k in A067874.

%C (End)

%H Robert Israel, <a href="/A089632/b089632.txt">Table of n, a(n) for n = 1..10000</a>

%e The prime factors of 35 are 5 and 7 and 5 * 7 + 1 = 36 is a square; so 35 belongs to the sequence.

%p filter:= n -> issqr(1+convert(numtheory:-factorset(n),`*`)):

%p select(filter, [$1..10000]); # _Robert Israel_, Apr 14 2019

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

%o (PARI) isok(n) =  my(f=factor(n)); issquare(1+prod(k=1, #f~, f[k,1])); \\ _Michel Marcus_, Apr 15 2019

%Y Cf. A089653. A091278 gives squares, A091279 gives square roots.

%Y Cf. A067874, A076618.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Jan 04 2004

%E More terms from _Ray Chandler_, Jan 05 2004