|
| |
|
|
A136548
|
|
For any integer the next smaller prime or one function: If n is an integer and greater than two then the function is the prime(m) such that n>prime(m) or if less than or equal to 2 it is defined as 1.
|
|
3
| |
|
|
1, 1, 2, 3, 3, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 29, 29, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 41, 41, 43, 43, 43, 43, 47, 47, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 61, 61, 61, 61, 61, 61, 67, 67, 67, 67, 71, 71
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| This sequence is related to the how often primes occur: n-f[n]
is always a positive number and greater than or equal to 1 for every number except 1 itself. It is closely related to the function gap[m]=Prime[m+1]-Prime[m]
a(n) = the largest number k such that A000203(k) <= n, where A000203(m) = sum of divisors of m. Example for n=7: a(7) = 5, before 5 is largest number k with A000203(k) <= 7. [From Jaroslav Krizek, Mar 01 2010]
a(n+1) = the largest numbers k such that A007955(k) <= n, where A007955(m) = product of divisors of m. Example for n=7: a(7+1) = a(8) = 7, before 7 is largest number k with A007955(k) <= 7. [From Jaroslav Krizek, Apr 01 2010]
|
|
|
LINKS
| Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000
|
|
|
FORMULA
| For n>2, a(n) = A000040(A000720((n-1)). [Enrique Pérez Herrero, Jul 23 2011]
|
|
|
MATHEMATICA
| A136548[1]:= 1; A136548[2]:= 1; A136548[n_]:= Prime[PrimePi[n-1]]; Array[A136548, 50] (* Enrique Pérez Herrero, Jul 23 2011 *)
|
|
|
CROSSREFS
| Cf. A000040, A000720
Sequence in context: A074399 A090302 A093074 * A007917 A151799 A093841
Adjacent sequences: A136545 A136546 A136547 * A136549 A136550 A136551
|
|
|
KEYWORD
| nonn,uned
|
|
|
AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 26 2008
|
| |
|
|
