A176686 -id:A176686 - cp's OEIS frontend

A176687 Numbers k such that k^2-1 is the product of 4 distinct primes.

34, 56, 86, 92, 94, 104, 106, 142, 144, 160, 164, 166, 184, 186, 194, 196, 202, 204, 214, 216, 218, 220, 230, 232, 236, 248, 256, 266, 272, 284, 300, 302, 304, 320, 322, 328, 340, 346, 358, 384, 392, 394, 398, 400, 412, 414, 416, 430, 434, 446, 452, 456, 464

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

nonn

			34 is in the sequence, because 34^2 - 1 = 1155 = 3 * 5 * 7 * 11, so it's a product of 4 distinct primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A006881, A007304, A014574, A046386, A176686

Select[Range[7! ],Last/@FactorInteger[ #^2-1]=={1,1,1,1}&]
dp4Q[n_]:=Module[{c=n^2-1},PrimeNu[c]==PrimeOmega[c]==4]; Select[Range[ 500], dp4Q] (* Harvey P. Dale, Dec 31 2013 *)

A272078 Numbers k such that k^2 + 1 is product of 3 distinct primes.

Original entry on oeis.org

13, 17, 21, 23, 27, 31, 33, 37, 53, 55, 63, 67, 72, 75, 77, 81, 87, 89, 91, 97, 98, 103, 105, 109, 111, 112, 113, 115, 119, 122, 125, 127, 128, 129, 135, 137, 138, 142, 147, 148, 149, 151, 153, 155, 161, 162, 163, 167, 172, 174, 179, 185, 189, 192, 197, 200, 208

Offset: 1

K. D. Bajpai, Apr 19 2016

nonn

			13 appears in the list because 13^2 + 1 = 170 = 2 * 5 * 17.
21 appears in the list because 21^2 + 1 = 442 = 2 * 13 * 17.

Daniel Starodubtsev, Table of n, a(n) for n = 1..1000

Cf. A007304, A046386, A176686, A176687.

A272078 = {}; Do[ k = Last /@ FactorInteger[n^2 + 1]; If[k == {1, 1, 1}, AppendTo[A272078, n]], {n, 1000}]; A272078
Select[Range[1000], Last /@ FactorInteger[#^2 + 1] == {1, 1, 1} &]

isok(k) = my(x=k^2+1); (omega(x)==3) && (bigomega(x)==3); \\ Michel Marcus, Mar 11 2020

cp's OEIS Frontend

A176687 Numbers k such that k^2-1 is the product of 4 distinct primes.

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