OFFSET
2,1
COMMENTS
All terms are squarefree. Many thanks to Michael Branicky for pointing out errors in the terms in the original submission.
FORMULA
(n-1)! <= a(n) <= A371194(n).
EXAMPLE
a(2) = 3 = 3 whose prime factors in base 2 is: 11.
a(3) = 5 = 5 whose prime factors in base 3 is: 12.
a(4) = 14 = 2*7 whose prime factors in base 4 is: 2, 13.
a(5) = 133 = 7*19 whose prime factors in base 5 is: 12, 34.
a(6) = 706 = 2*353 whose prime factors in base 6 is: 2, 1345.
a(7) = 2490 = 2*3*5*83 whose prime factors in base 7 is: 2, 3, 5, 146.
a(8) = 24258 = 2*3*13*311 whose prime factors in base 8 is: 2, 3, 15, 467.
a(9) = 217230 = 2*3*5*13*557 whose prime factors in base 9 is: 2, 3, 5, 14, 678.
a(10) = 2992890 = 2*3*5*67*1489.
a(11) = 24674730 = 2*3*5*19*73*593 whose prime factors in base 11 is: 2, 3, 5, 18, 67, 49a.
a(12) = 647850030 = 2*3*5*19*1136579 whose prime factors in base 12 is: 2, 3, 5, 17, 4698ab.
PROG
(Python)
from math import factorial
from itertools import count
from sympy import primefactors
from sympy.ntheory import digits
def A370612(n): return next(k for k in count(max(factorial(n-1), 2)) if 0 not in (s:=set.union(*(set(digits(p, n)[1:]) for p in primefactors(k)))) and len(s) == n-1)
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Chai Wah Wu, Apr 30 2024
STATUS
approved