A091278 -id:A091278 - cp's OEIS frontend

A091279 Square roots of A091278.

2, 2, 4, 2, 6, 4, 4, 2, 4, 12, 6, 14, 4, 2, 6, 16, 18, 4, 20, 4, 22, 14, 4, 2, 16, 6, 30, 14, 32, 4, 34, 20, 4, 6, 16, 36, 38, 22, 12, 40, 6, 14, 42, 12, 4, 4, 2, 16, 14, 52, 20, 54, 14, 32, 56, 58, 4, 22, 34, 20, 60, 4, 16, 38, 16, 22, 66, 6, 68, 40, 14, 70, 72, 14, 18, 4, 34, 4, 78, 6

Offset: 1

Ray Chandler, Jan 05 2004

nonn

Cf. A089632.

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

Original entry on oeis.org

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

Joseph L. Pe, Jan 04 2004

nonn

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)

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

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

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

Cf. A067874, A076618.

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

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

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

More terms from Ray Chandler, Jan 05 2004

cp's OEIS Frontend

A091279 Square roots of A091278.

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

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