A080404 - OEIS

%I #16 Mar 18 2026 23:38:48

%S 2,2,6,2,6,2,6,6,30,2,6,6,6,30,2,6,30,6,6,30,2,6,30,6,30,6,210,6,30,2,

%T 30,6,30,6,30,6,210,6,30,30,6,2,30,6,30,210,6,30,30,6,30,210,6,30,30,

%U 6,2,210,30,6,30,210,6,30,30,6,210,30,6,30,210,6,30,210,30,6,2,210,30,30,6

%N a(n)=A007947[A055932(n)]; the sequence consists of primorial numbers;.

%H Michael De Vlieger, <a href="/A080404/b080404.txt">Table of n, a(n) for n = 1..10000</a>

%t With[{P = FoldList[Times, Prime@ Range@ Max@ #]}, Map[P[[#]] &, #]] &@ Map[PrimeNu@ # &, Select[Range[10^4], Last[#] == Length[#] &@ PrimePi@ FactorInteger[#][[All, 1]] &]] (* _Michael De Vlieger_, Feb 06 2020 *)

%o (Python)

%o from math import prod

%o from itertools import count

%o from functools import lru_cache

%o from sympy import prime, integer_log, primorial, primefactors

%o from oeis_sequences.OEISsequences import bisection

%o def A080404(n):

%o     @lru_cache(maxsize=None)

%o     def g(x, m): return sum(g(x//(prime(m)**i), m-1) for i in range(1,integer_log(x, prime(m))[0]+1)) if m-1 else x.bit_length()-1

%o     def f(x):

%o         c = n+x

%o         for k in count(1):

%o             if primorial(k)>x:

%o                 break

%o             c -= g(x,k)

%o         return c

%o     return prod(primefactors(bisection(f,n+1,n+1))) # _Chai Wah Wu_, Mar 18 2026

%Y Cf. A007947, A002110, A055932.

%K nonn

%O 1,1

%A _Labos Elemer_, Mar 19 2003