

A093549


a(n) is the smallest number m such that each of the numbers m1, m and m+1 has n distinct prime divisors.


4




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[m1]]==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 m1, m and m+1 has 3 distinct prime divisors.


MATHEMATICA

a[n_] := (For[m=2, !(Length[FactorInteger[m1]]==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(mk)!=n&&(m+=2k)&&next(2)); return(m)) \\ M. F. Hasler, May 20 2014


CROSSREFS

Cf. A093550, A052215, A093548.
Sequence in context: A111432 A180999 A181003 * A012044 A098918 A001699
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



