The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A367014 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A367014

Let q be the n-th prime power (A246655), then a(n) = q^3 + q^2 - q; number of solutions to x*y = z*w in the finite field F_q.
(history; published version)

#19 by Joerg Arndt at Sun Jan 19 01:30:09 EST 2025

STATUS

reviewed

approved

#18 by Michel Marcus at Sun Jan 19 01:01:02 EST 2025

STATUS

proposed

reviewed

#17 by Chai Wah Wu at Sun Jan 19 00:59:57 EST 2025

STATUS

editing

proposed

#16 by Chai Wah Wu at Sun Jan 19 00:59:51 EST 2025

PROG

return kmax

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

return (m:=bisection(f, n, n))*(m*(m+1)-1) # Chai Wah Wu, Jan 19 2025

#15 by Chai Wah Wu at Sun Jan 19 00:59:32 EST 2025

PROG

(Python)

from sympy import primepi, integer_nthroot

def A367014(n):

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

return (m:=bisection(f, n, n))*(m*(m+1)-1) # Chai Wah Wu, Jan 19 2025

STATUS

approved

editing

#14 by Peter Luschny at Sun Nov 26 15:55:57 EST 2023

STATUS

reviewed

approved

#13 by Amiram Eldar at Sun Nov 26 14:41:14 EST 2023

STATUS

proposed

reviewed

#12 by Paolo Xausa at Sun Nov 26 14:33:56 EST 2023

STATUS

editing

proposed

#11 by Paolo Xausa at Sun Nov 26 14:33:32 EST 2023

MATHEMATICA

Map[#^3+#^2-#&, Select[Range[200], PrimePowerQ]] (* Paolo Xausa, Nov 26 2023 *)

STATUS

approved

editing

#10 by OEIS Server at Sat Nov 25 18:36:50 EST 2023

LINKS

Jianing Song, <a href="/A367014/b367014_1.txt">Table of n, a(n) for n = 1..10000</a>