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A180656 Squarefree semiprimes k such that (m+1)^2-k is also a square, where m = ceiling(sqrt(k)). 0
33, 39, 85, 119, 133, 253, 377, 403, 527, 629, 703, 943, 989, 1363, 1537, 1643, 2183, 2257, 2747, 2881, 3053, 3139, 3337, 3431, 4187, 4399, 4897, 5251, 5429, 6499, 6767, 6887, 6901, 7171, 7313, 7373, 7519, 7597, 7811, 7957, 8453, 8611, 8927, 9379, 11303 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Original name: Squarefree semiprimes k such that the second-next perfect square minus k is a perfect square.

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

3*11 = 33, 49-33 = 16 -> 4, 7-4 = 3, 7+4 = 11;

3*13 = 39, 64-39 = 25 -> 5, 8-5 = 3, 8+5 = 13.

MATHEMATICA

f1[n_] := Last/@FactorInteger[n] == {1, 1}; f2[n_] := IntegerQ[Sqrt[(Ceiling[Sqrt[n]] + 1)^2 - n]]; lst={}; Do[If[f1[n] && f2[n], AppendTo[lst, n]], {n, 8!}]; lst

PROG

(PARI) isok(k) = issquarefree(k) && (bigomega(k)==2) && issquare((ceil(sqrt(k))+1)^2-k); \\ Michel Marcus, Nov 27 2019

CROSSREFS

Cf. A006881, A180655.

Sequence in context: A039326 A043149 A043929 * A034070 A168311 A045241

Adjacent sequences:  A180653 A180654 A180655 * A180657 A180658 A180659

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Sep 15 2010

EXTENSIONS

Original name replaced (using an Apr 19 2012 Comments entry from M. F. Hasler) by Jon E. Schoenfield, Nov 25 2019

STATUS

approved

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Last modified December 7 05:26 EST 2021. Contains 349567 sequences. (Running on oeis4.)