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A062320
Nonsquarefree numbers squared. A013929(n)^2.
4
16, 64, 81, 144, 256, 324, 400, 576, 625, 729, 784, 1024, 1296, 1600, 1936, 2025, 2304, 2401, 2500, 2704, 2916, 3136, 3600, 3969, 4096, 4624, 5184, 5625, 5776, 6400, 6561, 7056, 7744, 8100, 8464, 9216, 9604, 9801, 10000, 10816, 11664, 12544, 13456
OFFSET
1,1
COMMENTS
A008966(A037213(a(n))) = 0. - Reinhard Zumkeller, Sep 03 2015
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = Pi^2/6 - 15/Pi^2. - Amiram Eldar, Jul 16 2020
PROG
(PARI) for(n=1, 55, if(issquarefree(n), n+1, print(n^2)))
(PARI) n=-1; for (m=1, 10^9, if (!issquarefree(m), write("b062320.txt", n++, " ", m^2); if (n==1000, break))) \\ Harry J. Smith, Aug 04 2009
(PARI) is(n)=issquare(n, &n) && !issquarefree(n) \\ Charles R Greathouse IV, Sep 18 2015
(Haskell)
a062320 = (^ 2) . a013929 -- Reinhard Zumkeller, Sep 03 2015
(Python)
from math import isqrt
from sympy import mobius
def A062320(n):
def f(x): return n+1+sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1))
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
return bisection(f)**2 # Chai Wah Wu, Aug 31 2024
CROSSREFS
Squares in A046099.
Sequence in context: A092210 A320892 A365263 * A233330 A370787 A322449
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jul 05 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jul 11 2001
Offset corrected by Andrew Howroyd, Sep 18 2024
STATUS
approved