login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A154704 a(n) = smallest number k such that k-1 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 (list; graph; refs; listen; history; text; internal format)
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, k-1 = 3 and k+1 = 5 (twin primes) both have one factor and 4 is the smallest such number.

For k = 55, k-1 = 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, k-1 = 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(k-1) ] 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 9 10:29 EDT 2021. Contains 343732 sequences. (Running on oeis4.)