

A154704


a(n) = smallest number k such that k1 and k+1 both have n prime divisors (counted with multiplicity).


3



4, 5, 19, 55, 271, 1889, 10529, 59777, 101249, 406783, 6581249, 12164095, 65071999, 652963841, 6548416001, 13858918399, 145046192129, 75389157377, 943344975871, 23114453401601, 108772434771967, 101249475018751, 551785225781249
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OFFSET

1,1


COMMENTS

Similar to A154598, where k is restricted to primes.


LINKS

Table of n, a(n) for n=1..23.


EXAMPLE

For k = 4, k1 = 3 and k+1 = 5 (twin primes) both have one factor and 4 is the smallest such number.
For k = 55, k1 = 54 = 2*3*3*3 and k+1 = 56 = 2*2*2*7 both have four factors and 55 is the smallest such number.
For k = 59777, k1 = 59776 = 2*2*2*2*2*2*2*467 and k+1 = 59778 = 2*3*3*3*3*3*3*41 both have eight factors and 59777 is the smallest such number.


PROG

(MAGMA) S:=[]; for n:=1 to 10 do k:=3; while not &+[ f[2]: f in Factorization(k1) ] eq n or not &+[ f[2]: f in Factorization(k+1) ] eq n do k+:=1; end while; Append(~S, k); end for; S;


CROSSREFS

Cf. A154598, Cf. A001222 (number of prime divisors of n).
Sequence in context: A136211 A041036 A041699 * A047023 A032319 A041255
Adjacent sequences: A154701 A154702 A154703 * A154705 A154706 A154707


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Jan 14 2009, Jan 15 2009


EXTENSIONS

a(15)a(23) from Donovan Johnson, Jan 21 2009


STATUS

approved



