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A373965
Numbers k such that k^2 is in A086539.
1
1, 3, 5, 11, 17, 25, 29, 41, 43, 53, 61, 67, 71, 79, 83, 97, 101, 103, 109, 113, 127, 131, 139, 149, 151, 157, 163, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 233, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 311, 313, 317, 331, 337, 347, 349, 353, 359, 373, 379, 383, 389, 397, 401, 409
OFFSET
1,2
COMMENTS
Are 1 and 25 the only terms that are not primes?
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..430 (terms 1..150 from Robert Israel)
EXAMPLE
a(3) = 5 is a term because 5^2 = 25 = A086539(13).
MAPLE
R:= 1, 2: x:= 2: S:= 1: nS:= 1:
for n from 3 do
t:= ilcm(R[ceil(n/2).. n-1]);
for i from x+1 while igcd(i, t) <> 1 do od:
R:= R, i;
x:= i;
if issqr(i) then
nS:= nS+1; s:= sqrt(i); S:= S, s;
if nS = 100 then break fi
fi;
od:
S;
PROG
(Python)
from math import gcd
from itertools import count, islice
from sympy import integer_nthroot
def A373965_gen(): # generator of terms
alist, a, b = [1], 1, False
yield 1
while True:
for m in count(a+1):
if all(gcd(m, d) == 1 for d in alist):
if (x:=integer_nthroot(a:=m, 2))[1]: yield x[0]
alist = alist[(b:=not b):]+[a]
break
A373965_list = list(islice(A373965_gen(), 40)) # Chai Wah Wu, Jun 25 2024
CROSSREFS
Cf. A086539.
Sequence in context: A258713 A267517 A309427 * A211435 A049752 A371165
KEYWORD
nonn
AUTHOR
Robert Israel, Jun 23 2024
STATUS
approved