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

1,1

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)

Links

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

Example

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

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]] &]

Prog

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

Crossrefs

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

Cf. A067874, A076618.

Sequence in context: A249734 A319316 A087031 * A247643 A287351 A256388

Adjacent sequences: A089629 A089630 A089631 * A089633 A089634 A089635

Keyword

nonn

Author

Joseph L. Pe, Jan 04 2004

Extensions

More terms from Ray Chandler, Jan 05 2004

Status

approved