A231968 Squarefree numbers (A005117) of the form p*q*r*s with prime factors p, q, r, s with q = 2*p + 1, r = 2*q + 1 and s = 2*r + 1.

2530, 59455, 4112125651, 66487065301, 1069364586601, 4313828719351, 146264252084551, 252626415665851, 3398860950259501, 10045301361318901, 110736954977078251, 804798055395768151, 1138773641873001751, 1287533822935708351, 1380776111154106201, 5548832990383854601, 9657954525580111351

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Formula

a(n) = A023272(n) * (2*A023272(n) + 1) * (4*A023272(n) + 3) * (8*A023272(n) + 7). - Robert Israel, Dec 17 2025

Example

4112125651 = 89*179*359*719; 179 = 2*89 + 1; 359 = 2*179 + 1, 719 = 2*359 + 1.

Maple

p:= 1: R:= NULL: count:= 0:
while count < 100 do
  p:= nextprime(p);
  if isprime(2*p+1) and isprime(4*p+3) and isprime(8*p+7) then
    count:= count+1; R:= R, p*(2*p+1)*(4*p+3)*(8*p+7);
  fi
od:
R; # Robert Israel, Dec 17 2025

Crossrefs

Cf. A005117, A000040, A023272, A231967, A231969, A231966.

Sequence in context: A268332 A369521 A203440 * A172142 A206596 A334932

Adjacent sequences: A231965 A231966 A231967 * A231969 A231970 A231971

Keyword

nonn

Author

Jaroslav Krizek, Nov 18 2013

Extensions

More terms from Robert Israel, Dec 17 2025

Status

approved