OFFSET
1,1
COMMENTS
Since A119479(8)=7, there are never more than 7 consecutive terms. Runs of 7 consecutive terms start at 171897, 180969, 647385, ... (subsequence of A049053). - Ivan Neretin, Feb 08 2016
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from R. J. Mathar)
Jérôme Germoni, Nombres à huit diviseurs, Images des Mathématiques, CNRS, 2017 (in French).
Eric Weisstein's World of Mathematics, Divisor Product.
FORMULA
A000005(a(n))=8. - Juri-Stepan Gerasimov, Oct 10 2009
MAPLE
select(numtheory:-tau=8, [$1..1000]); # Robert Israel, Dec 17 2014
MATHEMATICA
Select[Range[400], DivisorSigma[0, #]== 8 &] (* Vincenzo Librandi, Oct 05 2017 *)
PROG
(PARI) Vec(select(x->x==8, vector(500, i, numdiv(i)), 1)) \\ Michel Marcus, Dec 17 2014
(Magma) [n: n in [1..400] | DivisorSigma(0, n) eq 8]; // Vincenzo Librandi, Oct 05 2017
(Python)
from sympy import divisor_count
isok = lambda n: divisor_count(n) == 8
print([n for n in range(1, 400) if isok(n)]) # Darío Clavijo, Oct 17 2023
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A030626(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(primepi(x//(k*m))-b for a, k in enumerate(primerange(integer_nthroot(x, 3)[0]+1), 1) for b, m in enumerate(primerange(k+1, isqrt(x//k)+1), a+1))-sum(primepi(x//p**3) for p in primerange(integer_nthroot(x, 3)[0]+1))+primepi(integer_nthroot(x, 4)[0])-primepi(integer_nthroot(x, 7)[0]))
return bisection(f, n, n) # Chai Wah Wu, Feb 21 2025
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
STATUS
approved