A089632 1 + product of prime factors of n is a perfect square.

3, 9, 15, 27, 35, 45, 75, 81, 135, 143, 175, 195, 225, 243, 245, 255, 323, 375, 399, 405, 483, 585, 675, 729, 765, 875, 899, 975, 1023, 1125, 1155, 1197, 1215, 1225, 1275, 1295, 1443, 1449, 1573, 1599, 1715, 1755, 1763, 1859, 1875, 2025, 2187, 2295, 2535

Offset: 1

Author

Joseph L. Pe, Jan 04 2004

Keywords

• nonn

Comments

From Robert Israel, Apr 14 2019: (Start)

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

All terms are odd.

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

(End)

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Cf. A067874, A076618.

Programs

Maple

filter:= n -> issqr(1+convert(numtheory:-factorset(n),`*`)):
select(filter, [$1..10000]); # Robert Israel, Apr 14 2019

Mathematica

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

PARI

isok(n) =  my(f=factor(n)); issquare(1+prod(k=1, #f~, f[k,1])); \\ Michel Marcus, Apr 15 2019

Extensions

More terms from Ray Chandler, Jan 05 2004