

A128281


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.


6




OFFSET

1,1


COMMENTS

From Iain Fox, Aug 26 2020: (Start)
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(6) > 2*10^11 if it exists.  David A. Corneth, Aug 27 2020
a(n) >= A070826(n+1) by definition of the sequence.  Iain Fox, Aug 28 2020


LINKS

Table of n, a(n) for n=1..5.


EXAMPLE

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.


PROG

(PARI) a(n)=if(n==1, return(3)); my(p=prod(k=1, n, prime(k+1))); forstep(m=p+if(p%41, 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


CROSSREFS

Subsequence of A076274.
Lower bound: A070826.
Cf. A002145, A128276, A128282, A128283, A128284, A128285, A128286, A168352.
Sequence in context: A306093 A076207 A134057 * A034268 A140451 A054147
Adjacent sequences: A128278 A128279 A128280 * A128282 A128283 A128284


KEYWORD

nonn,hard,more


AUTHOR

Kok Seng Chua (chuakokseng(AT)hotmail.com), Mar 05 2007


EXTENSIONS

Definition corrected by Iain Fox, Aug 25 2020


STATUS

approved



