The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A267697 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A267697

Numbers with 7 odd divisors.
(history; published version)

#40 by Joerg Arndt at Sat Feb 22 01:23:07 EST 2025

STATUS

reviewed

approved

#39 by Michel Marcus at Sat Feb 22 00:52:55 EST 2025

STATUS

proposed

reviewed

#38 by Chai Wah Wu at Sat Feb 22 00:46:29 EST 2025

STATUS

editing

proposed

#37 by Chai Wah Wu at Sat Feb 22 00:46:14 EST 2025

PROG

return bisection(f, n, n) # Chai Wah Wu, Feb 22 2025

#36 by Chai Wah Wu at Sat Feb 22 00:46:01 EST 2025

PROG

(Python)

from sympy import integer_log, primerange, integer_nthroot

def A267697(n):

def bisection(f, kmin=0, kmax=1):

while f(kmax) > kmax: kmax <<= 1

kmin = 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(integer_log(x//p**6, 2)[0]+1 for p in primerange(3, integer_nthroot(x, 6)[0]+1)))

return bisection(f, n, n) # Chai Wah Wu, Feb 22 2025

STATUS

approved

editing

#35 by Joerg Arndt at Mon Sep 16 02:10:21 EDT 2024

STATUS

reviewed

approved

#34 by Hugo Pfoertner at Mon Sep 16 02:06:30 EDT 2024

STATUS

proposed

reviewed

#33 by Amiram Eldar at Mon Sep 16 01:07:22 EDT 2024

STATUS

editing

proposed

#32 by Amiram Eldar at Mon Sep 16 01:06:05 EDT 2024

COMMENTS

Numbers n k such that the symmetric representation of sigma(nk) has 7 subparts. - Omar E. Pol, Dec 28 2016

#31 by Amiram Eldar at Mon Sep 16 00:38:29 EDT 2024

FORMULA

Sum_{n>=1} 1/a(n) = 2 * P(6) - 1/32 = 0.00289017370127..., where P(6) is the value of the prime zeta function at 6 (A085966). - Amiram Eldar, Sep 16 2024

CROSSREFS

Cf. A001227, A030516, A038547, A085966, A236104, A237593, A279387.

STATUS

approved

editing