The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A072775

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Showing entries 1-10 | older changes

A072775

Squarefree kernels of powers of squarefree numbers.
(history; published version)

#12 by Joerg Arndt at Mon Aug 19 02:20:49 EDT 2024

STATUS

reviewed

approved

#11 by Michel Marcus at Mon Aug 19 01:46:16 EDT 2024

STATUS

proposed

reviewed

#10 by Chai Wah Wu at Mon Aug 19 00:36:08 EDT 2024

STATUS

editing

proposed

#9 by Chai Wah Wu at Mon Aug 19 00:36:03 EDT 2024

PROG

return prod(primefactors(kmax)) # Chai Wah Wu, Aug 19 2024

#8 by Chai Wah Wu at Mon Aug 19 00:35:49 EDT 2024

PROG

(Python)

from math import isqrt, prod

from sympy import mobius, integer_nthroot, primefactors

def A072775(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 prod(primefactors(kmax)) # Chai Wah Wu, Aug 19 2024

STATUS

approved

editing

#7 by Reinhard Zumkeller at Sun Apr 06 10:23:04 EDT 2014

STATUS

editing

approved

#6 by Reinhard Zumkeller at Sun Apr 06 07:33:05 EDT 2014

PROG

(Haskell)

a072775 n = a072775_list !! (n-1) -- a072775_list defined in A072774.

-- Reinhard Zumkeller, Apr 06 2014

CROSSREFS

Cf. A052410.

#5 by Reinhard Zumkeller at Sun Apr 06 07:31:12 EDT 2014

LINKS

Reinhard Zumkeller, <a href="/A072775/b072775.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 18:50:24 EDT 2012

AUTHOR

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Jul 10 2002

Discussion

Fri Mar 30

18:50

OEIS Server: https://oeis.org/edit/global/246

#3 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Square-free Squarefree kernels of powers of square-free squarefree numbers.

COMMENTS

A072774(n) is square-free squarefree iff A072774(n)=a(n).

KEYWORD

nonn,new

nonn