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.
Chai Wah Wu, Algorithms for Complementary Sequences, Integers (2025) Vol. 25, Art. No. A95. See p. 24.
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
AUTHOR
STATUS
approved
