A168352 Products of 6 distinct odd primes.

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

Author

Vladimir Joseph Stephan Orlovsky, Nov 23 2009

Keywords

• nonn
• easy

Examples

			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
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005408, A067885.

Cf. A046391 (5 distinct odd primes).

Programs

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

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

Formula

A067885 INTERSECT A005408. [R. J. Mathar, Nov 24 2009]

Extensions

Definition corrected by R. J. Mathar, Nov 24 2009

More terms from David A. Corneth, Aug 26 2020