A072776 - OEIS

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A072776

Exponents of powers of squarefree numbers.

5

1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

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OFFSET

1,4

COMMENTS

A072774(n) = A072775(n)^a(n);

A072774(n) is squarefree iff a(n)=1.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

PROG

(Haskell)

a072776 n = a072776_list !! (n-1) -- a072776_list defined in A072774.

-- Reinhard Zumkeller, Apr 06 2014

(Python)

from math import isqrt

from sympy import mobius, integer_nthroot, perfect_power

def A072776(n):

def g(x): return int(sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1)))-1

def f(x): return n-2+x-sum(g(integer_nthroot(x, k)[0]) for k in range(1, x.bit_length()))

kmin, kmax = 1, 2

while f(kmax) >= kmax:

kmax <<= 1

while True:

kmid = kmax+kmin>>1

if f(kmid) < kmid:

kmax = kmid

else:

kmin = kmid

if kmax-kmin <= 1:

break

return 1 if not (p:=perfect_power(kmax)) else p[1] # Chai Wah Wu, Aug 19 2024

CROSSREFS

Sequence in context: A373835 A373369 A319864 * A077481 A278113 A242012

Adjacent sequences: A072773 A072774 A072775 * A072777 A072778 A072779

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jul 10 2002

STATUS

approved