OFFSET
1,1
COMMENTS
Also numbers n such that the product of proper divisors is < n.
See A050216 for lengths of blocks of consecutive primes. - Reinhard Zumkeller, Sep 23 2011
Numbers q > 1 such that d(q) < 4. Numbers k such that the number of ways of writing k = m + t is equal to the number of ways of writing k = r*s, where m|t and r|s. - Juri-Stepan Gerasimov, Oct 14 2017
Called multiplicatively deficient numbers by Chau (2004). - Amiram Eldar, Jun 29 2022
REFERENCES
F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House 2000
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
William Chau, The tau, sigma, rho functions, and some related numbers, Pi Mu Epsilon Journal, Vol. 11, No. 10 (Spring 2004), pp. 519-534; entire issue.
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
FORMULA
A109810(a(n)) = 2. - Reinhard Zumkeller, May 24 2010
A056595(a(n)) = 1. - Reinhard Zumkeller, Aug 15 2011
The number of terms not exceeding x is N(x) ~ (x + 2*sqrt(x))/log(x) (Chau, 2004). - Amiram Eldar, Jun 29 2022
MATHEMATICA
nn = 223; t = Union[Prime[Range[PrimePi[nn]]], Prime[Range[PrimePi[Sqrt[nn]]]]^2] (* T. D. Noe, Apr 11 2011 *)
Module[{upto=250, prs}, prs=Prime[Range[PrimePi[upto]]]; Select[Join[ prs, prs^2], #<=upto&]]//Sort (* Harvey P. Dale, Oct 08 2016 *)
PROG
(Haskell)
a000430 n = a000430_list !! (n-1)
a000430_list = m a000040_list a001248_list where
m (x:xs) (y:ys) | x < y = x : m xs (y:ys)
| x > y = y : m (x:xs) ys
-- Reinhard Zumkeller, Sep 23 2011
(PARI) is(n)=isprime(n) || (issquare(n, &n) && isprime(n)) \\ Charles R Greathouse IV, Sep 04 2013
(Python)
from math import isqrt
from sympy import primepi
def A000430(n):
def f(x): return n+x-primepi(x)-primepi(isqrt(x))
m, k = n, f(n)
while m != k:
m, k = k, f(k)
return int(m) # Chai Wah Wu, Aug 09 2024
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
R. Muller
STATUS
approved