cp's OEIS Frontend

A365435 Position of A002110(n) in A005117.

%I A365435 #29 Aug 13 2024 21:03:54
%S A365435 1,2,5,19,129,1405,18262,310347,5896728,135624240,3933101824,
%T A365435 121926157641,4511267827532,184961980943493,7953365180610401,
%U A365435 373808163488684050,19811832664899731266,1168898127229083969893,71302785760974119699474
%N A365435 Position of A002110(n) in A005117.
%C A365435 Primorial A002110(n) is the a(n)-th squarefree number.
%e A365435 Let b(n) = A002110(n) and c(n) = A005117(n).
%e A365435 a(0) = 1 since b(0) = 1, and c(1) = 1.
%e A365435 a(1) = 2 since b(1) = 2 = c(2).
%e A365435 a(2) = 5 since b(2) = 6 = c(5).
%e A365435 a(3) = 19 since b(3) = 30 = c(19), etc.
%t A365435 s = Select[Range[2^20], SquareFreeQ]; Map[FirstPosition[s, #][[1]] &, FoldList[Times, 1, Prime@ Range[7]] ]
%o A365435 (PARI) A071172(n) = my(s); forsquarefree(d=1, sqrtint(n), s += n\d[1]^2 * moebius(d)); s; \\ _Charles R Greathouse IV_ at A071172
%o A365435 a(n) = my(p = prod(i = 1, n, prime(i))); A071172(p); \\ _Amiram Eldar_, Nov 19 2023
%o A365435 (Python)
%o A365435 from math import isqrt
%o A365435 from sympy import primorial, mobius
%o A365435 def A365435(n):
%o A365435     if n == 0: return 1
%o A365435     p = primorial(n)
%o A365435     return sum(mobius(k)*(p//k**2) for k in range(1,isqrt(p)+1)) # _Chai Wah Wu_, Aug 12 2024
%Y A365435 Cf. A002110, A005117, A071172.
%K A365435 nonn,hard,more
%O A365435 0,2
%A A365435 _Michael De Vlieger_, Nov 19 2023
%E A365435 a(8)-a(16) from _Amiram Eldar_, Nov 19 2023
%E A365435 a(17) from _Chai Wah Wu_, Aug 12 2024
%E A365435 a(18) from _Chai Wah Wu_, Aug 13 2024