

A078502


a(n) = smallest positive integer N such that (N  k)/k is prime for k = 1, 2, ..., n.


2



3, 6, 12, 12, 174600, 7224840, 10780560, 10780560, 1086338816640, 50060257410240, 7720634052774720, 227457297898150320, 7272877497848202240, 7272877497848202240
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OFFSET

1,1


COMMENTS

The idea for the sequence and first eleven terms are from Ken Wilke.
a(n) == 0 (mod 120) for n > 4: because a(n)/2, a(n)/3, a(n)/4 and a(n)/5 must be integer, a(n) == 0 (mod 60); and if a(n) == 60 (mod 120), (a(n)4)/4 == 14 (mod 120) would not be prime; thus a(n) == 0 (mod 120). A more general result is a(n) == 0 (mod lcm(1,2,...,n)) for all n >= 1, and a(n) == 0 (mod 2*lcm(1,2,...,n)) for n > 4.  JeanChristophe Hervé, Sep 15 2014


LINKS



FORMULA



EXAMPLE

(12k)/k is prime for k = 1,2,3,4 and 12 is the smallest positive integer satisfying this property. Hence a(4) = 12.


PROG

(PARI)
a(n)=k=1; while(k, c=0; for(i=1, n, if(k%i==0&&isprime(k/i1), c++)); if(c==n, return(k)); k++)
n=1; while(n<10, print1(a(n), ", "); n++) \\ Derek Orr, Sep 15 2014


CROSSREFS

Cf. A074200 (equivalent sequence for (N+k)/k prime).


KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



