|
|
A254625
|
|
Integers n such that core(n), core(n+1), core(n+2) are smaller than n^(1/3) where core(n) is A007913(n), the squarefree part of n.
|
|
1
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Theorem 2 in Rouse & Yang link proves that this sequence is infinite.
|
|
LINKS
|
|
|
EXAMPLE
|
48 is a term since core(48)=3, core(49)=1, core(50)=2, these 3 values being smaller than 48^(1/3).
|
|
PROG
|
(PARI) isok(n) = my(cb = sqrtnint(n, 3)); (core(n) <= cb) && (core(n+1) <= cb) && (core(n+2) <= cb);
(PARI) /* This program is a little sloppy in testing more points than needed near the start and end, but adding extra code to avoid this case would add to complexity without greatly affecting runtime. */
list(lim, startAt=27)=my(c0, c1, c2); for(c=sqrtnint(startAt\1, 3), ceil(sqrtn(lim, 3)), my(n=c^3+1, lm=(c+1)^3); while(n<lm, if(isprime(n+1), n+=2; next); if(isprime(n), n++; next); c2=core(n+2); if(c2>c, n+=3; next); c1=core(n+1); if(c1>c, n+=2; next); c0=core(n); if(c0>c, n++; next); print1(n", "); n++)) \\ Charles R Greathouse IV, Jul 16 2015
(Python)
from operator import mul
from functools import reduce
from sympy import factorint
....return reduce(mul, [1]+[p for p, e in factorint(n).items() if e % 2])
A254625_list, n, c0, c1, c2 = [], 1, 1, 8, 27
for _ in range(10**6):
....if max(c0, c1, c2) < n:
....n += 1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|