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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. 2
1859, 357911, 2141399, 4641629, 6633419, 8447039, 10338119, 13526009, 20163059, 21603425, 24099569, 26187119, 26483321, 28226549, 33379569, 33485139, 40790009, 50139819, 52046075, 56152179, 57170075, 59824925, 72541799 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)