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A089632
1 + product of prime factors of n is a perfect square.
4
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
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.
Sequence in context: A249734 A319316 A087031 * A247643 A287351 A256388
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Jan 04 2004
EXTENSIONS
More terms from Ray Chandler, Jan 05 2004
STATUS
approved