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A128281
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a(n) is the least product of n distinct odd primes m=p_1*p_2*...*p_n, such that (d+m/d)/2 are all primes for each d dividing m.
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6
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OFFSET
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1,1
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COMMENTS
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a(6) > 10^9 if it exists.
All terms are members of A076274 since the definition requires that (1+m)/2 be prime.
The number of prime factors of m congruent to 3 (mod 4) must be even except for n=1.
(End)
a(n) >= A070826(n+1) by definition of the sequence. - Iain Fox, Aug 28 2020
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LINKS
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EXAMPLE
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105=3*5*7, (3*5*7+1)/2=53, (3+5*7)/2=19, (5+3*7)/2=13, (7+3*5)/2=11 are all primes and 105 is the least such number which is the product of 3 primes, so a(3)=3.
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PROG
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(PARI) a(n)=if(n==1, return(3)); my(p=prod(k=1, n, prime(k+1))); forstep(m=p+if(p%4-1, 2), +oo, 4, if(bigomega(m)==n && omega(m)==n, fordiv(m, d, if(!isprime((d+m/d)/2), next(2))); return(m))) \\ Iain Fox, Aug 27 2020
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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Kok Seng Chua (chuakokseng(AT)hotmail.com), Mar 05 2007
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EXTENSIONS
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Definition corrected by Iain Fox, Aug 25 2020
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STATUS
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approved
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