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

1,1

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

Links

Table of n, a(n) for n=1..8.

Formula

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

Example

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.

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}]

Prog

(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

Crossrefs

Cf. A093550, A052215, A093548.

Sequence in context: A111432 A180999 A181003 * A012044 A350513 A098918

Adjacent sequences: A093546 A093547 A093548 * A093550 A093551 A093552

Keyword

more,nonn

Author

Farideh Firoozbakht, Apr 07 2004

Extensions

a(7) from Donovan Johnson, Apr 07 2008

a(8) from Donovan Johnson, Jan 15 2009

Status

approved