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A168352
Products of 6 distinct odd primes.
3
255255, 285285, 345345, 373065, 435435, 440895, 451605, 465465, 504735, 533715, 555555, 569415, 596505, 608685, 615615, 636405, 645645, 672945, 680295, 692835, 705705, 719355, 726495, 752115, 770385, 780045, 795795, 803985, 805035, 811965, 823515, 838695, 844305, 858585
OFFSET
1,1
LINKS
FORMULA
A067885 INTERSECT A005408. [R. J. Mathar, Nov 24 2009]
EXAMPLE
255255 = 3*5*7*11*13*17
285285 = 3*5*7*11*13*19
345345 = 3*5*7*11*13*23
435435 = 3*5*7*11*13*29
MATHEMATICA
f[n_]:=Last/@FactorInteger[n]=={1, 1, 1, 1, 1, 1}&&FactorInteger[n][[1, 1]]>2; lst={}; Do[If[f[n], AppendTo[lst, n]], {n, 6*9!}]; lst
PROG
(PARI) is(n) = {n%2 == 1 && factor(n)[, 2]~ == [1, 1, 1, 1, 1, 1]} \\ David A. Corneth, Aug 26 2020
(Python)
from sympy import primefactors, factorint
print([n for n in range(1, 1000000, 2) if len(primefactors(n)) == 6 and max(list(factorint(n).values())) == 1]) # Karl-Heinz Hofmann, Mar 01 2023
(Python)
from math import prod, isqrt
from sympy import primerange, integer_nthroot, primepi
def A168352(n):
def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b+1, isqrt(x//c)+1), a+1)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b+1, integer_nthroot(x//c, m)[0]+1), a+1) for d in g(x, a2, b2, c*b2, m-1)))
def f(x): return int(n+x-sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 1, 2, 1, 6)))
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
return bisection(f, n, n) # Chai Wah Wu, Sep 10 2024
CROSSREFS
Cf. A046391 (5 distinct odd primes).
Sequence in context: A140079 A321505 A034631 * A147579 A087025 A249915
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Definition corrected by R. J. Mathar, Nov 24 2009
More terms from David A. Corneth, Aug 26 2020
STATUS
approved