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 A120810 Integers of the form p*q*r in A120806: x+d+1 is prime for all divisors d of x, where p, q and r are distinct odd primes. See A007304. 1
 935, 305015, 2339315, 3690185, 14080121, 14259629, 16143005, 17754869, 18679409, 26655761, 29184749, 47372135, 80945699, 82768529, 87102509 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA a(n) = n-th element of A120806 of the form p*q*r where p, q and r are distinct odd primes. EXAMPLE a(1)=935 since x=5*11*17, divisors(x)={1,5,11,17,5*11,5*17,11*17,5*11*17} and x+d+1={937, 941, 947, 953, 991, 1021, 1123, 1871} 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; if x mod 6 = 5 and 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, A007304, A120809, A120808, A120807. Sequence in context: A232380 A029570 A278186 * A027554 A259891 A282382 Adjacent sequences:  A120807 A120808 A120809 * A120811 A120812 A120813 KEYWORD nonn AUTHOR Walter Kehowski, Jul 06 2006 STATUS approved

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