|
Search: id:A089189
|
|
|
| A089189 |
|
Primes p such that p-1 is cube- or higher power-free. |
|
+0
2
|
|
| 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 79, 83, 97, 101, 103, 107, 113, 127, 131, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 257, 263, 269, 277, 283, 293, 307, 311, 317, 331, 337
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The ratio of the count of primes p <= n such that p-1 is cube-free to the count of primes <= n converges to 0.69.. . This implies that roughly 70% of the primes less one are cube-free. This compares to about 0.37 of the primes less one are square-free.
|
|
EXAMPLE
|
43 is included because 43-1 = 2*3*7. 41 is omitted because 41-1 = 2^3*5.
97 is omitted because 96 = 2^5*3 since higher powers are also tested for
exclusion.
|
|
PROGRAM
|
(PARI) powerfreep(n, p) = { c=0; pc=0; forprime(x=2, n, pc++; if(ispowerfree(x-1, p), c++; \ print1(x", "); ) ); print(); print(c", "pc", "c/pc+.0) } ispowerfree(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] >= p1, flag=0; break); ); return(flag) }
|
|
CROSSREFS
|
Sequence in context: A109611 A078133 A167773 this_sequence A038612 A012883 A002267
Adjacent sequences: A089186 A089187 A089188 this_sequence A089190 A089191 A089192
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), Dec 08 2003
|
|
|
Search completed in 0.002 seconds
|
