A093549 a(n) is the smallest number m such that each of the numbers m-1, m and m+1 has n distinct prime divisors.

3, 21, 645, 37961, 1042405, 323567035, 30989984675, 10042712381261

Offset: 1

Author

Farideh Firoozbakht, Apr 07 2004

Keywords

• more
• nonn

Comments

a(n) <= A093550(n) since here the factors do not occur necessarily to the first power, e.g. a(2)-1 = 20 = 2^2*5, therefore A093550(2) > a(2). - M. F. Hasler, May 20 2014

Examples

			a(3)=645 because 644=2^2*7*23; 645=3*5*43; 646=2*17*19 and 645 is the smallest number m such that each of the numbers m-1, m and m+1 has 3 distinct prime divisors.
		

Crossrefs

Cf. A093550, A052215, A093548.

Programs

Mathematica

a[n_] := (For[m=2, !(Length[FactorInteger[m-1]]==n && Length[FactorInteger[m]]==n&&Length[FactorInteger[m+1]]==n), m++ ];m);Do[Print[a[n]], {n, 7}]

PARI

a(n,m=2)=until(,for(k=-1,1,omega(m-k)!=n&&(m+=2-k)&&next(2));return(m)) \\ M. F. Hasler, May 20 2014

Formula

a[n_] := (For[m=2, !(Length[FactorInteger[m-1]]==n && Length[FactorInteger[m]]==n&&Length[FactorInteger[m+1]]==n), m++ ];m)

Extensions

a(7) from Donovan Johnson, Apr 07 2008

a(8) from Donovan Johnson, Jan 15 2009