A120809 Integers of the form p^2*q in A120806: x+d+1 is prime for all divisors d of x. Both p and q are odd primes, with p and q distinct. See A054753.

1859, 357911, 2141399, 4641629, 6633419, 8447039, 10338119, 13526009, 20163059, 21603425, 24099569, 26187119, 26483321, 28226549, 33379569, 33485139, 40790009, 50139819, 52046075, 56152179, 57170075, 59824925, 72541799

Offset

1,1

Links

Table of n, a(n) for n=1..23.

Formula

a(n) = n-th element of A120806 of the form p^2*q where p and q are distinct odd primes.

Example

a(1)=1859 since x=11*13^2, divisors(x)={1,11,13,11*13,13^2,11*13^2} and x+d+1={1861,1871,1873,2003,2029,3719} are all prime.

Maple

with(numtheory); is3almostprime := proc(n) local L; if n in [0, 1] or isprime(n) then return false fi; L:=ifactors(n)[2]; if nops(L) in [1, 2, 3] and convert(map(z-> z[2], L), `+`) = 3 then return true else return false fi; end; L:=[]: for w to 1 do for k from 1 while nops(L)<=50 do x:=2*k+1; y:=simplify(x^(1/3)); if x mod 6 = 5 and not type(y, integer) #clunky and not issqrfree(x) and is3almostprime(x) and andmap(isprime, [x+2, 2*x+1]) then S:=divisors(x); Q:=map(z-> x+z+1, S); if andmap(isprime, Q) then L:=[op(L), x]; print(nops(L), ifactor(x)); fi; fi; od od;

Crossrefs

Cf. A120806, A054753.

Sequence in context: A064978 A202913 A159212 * A213868 A022062 A107526

Adjacent sequences: A120806 A120807 A120808 * A120810 A120811 A120812

Keyword

nonn

Author

Walter Kehowski, Jul 06 2006

Status

approved