This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071773 #55 May 21 2025 10:44:22
%S A071773 1,1,1,2,1,1,1,2,3,1,1,2,1,1,1,2,1,3,1,2,1,1,1,2,5,1,3,2,1,1,1,2,1,1,
%T A071773 1,6,1,1,1,2,1,1,1,2,3,1,1,2,7,5,1,2,1,3,1,2,1,1,1,2,1,1,3,2,1,1,1,2,
%U A071773 1,1,1,6,1,1,5,2,1,1,1,2,3,1,1,2,1,1,1,2,1,3,1,2,1,1,1,2,1,7,3,10,1,1,1,2
%N A071773 a(n) = gcd(rad(n), n/rad(n)), where rad(n) = A007947(n) is the squarefree kernel of n.
%C A071773 n is squarefree iff a(n)=1.
%C A071773 Product of primes dividing n more than once. - _Charles R Greathouse IV_, Aug 08 2013
%C A071773 Squarefree kernel of the square part of n. - _Peter Munn_, Jun 12 2020
%H A071773 Charles R Greathouse IV, <a href="/A071773/b071773.txt">Table of n, a(n) for n = 1..10000</a>
%H A071773 Vaclav Kotesovec, <a href="/A071773/a071773.jpg">Graph - the asymptotic ratio (10000 terms)</a>
%H A071773 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>.
%F A071773 a(n) = gcd(A007947(n), A003557(n)).
%F A071773 Multiplicative with p^e -> p^ceiling((e-1)/e), p prime.
%F A071773 a(n) = rad(n/rad(n)) = A007947(A003557(n)). - _Velin Yanev_, _Antti Karttunen_, Aug 20 2017, Nov 28 2017
%F A071773 a(n) = A007947(A057521(n)). - _Antti Karttunen_, Nov 28 2017
%F A071773 a(n) = A007947(A008833(n)). - _Peter Munn_, Jun 12 2020
%F A071773 a(n) = gcd(A003415(n), A007947(n)). - _Antti Karttunen_, Jan 02 2023
%F A071773 Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + 1/p^(2*s-1) - 1/p^(2*s)). - _Amiram Eldar_, Nov 09 2023
%F A071773 From _Vaclav Kotesovec_, May 06 2025: (Start)
%F A071773 Let f(s) = Product_{p prime} (1 - 1/p^(2*s) + 1/p^(4*s-1) - 1/p^(4*s-2)).
%F A071773 Dirichlet g.f.: zeta(s) * zeta(2*s-1) * f(s).
%F A071773 Sum_{k=1..n} a(k) ~ f(1) * n * (log(n) + 3*gamma - 1 + f'(1)/f(1)) / 2, where
%F A071773 f(1) = A065464 = Product_{p prime} (1 - 2/p^2 + 1/p^3) = 0.428249505677094440218765707581823546121298513355936144031901379532123...
%F A071773 f'(1) = f(1) * Sum_{p prime} 2*(3*p-2)*log(p) / (p^3-2*p+1) = f(1) * 2.939073481649229666406787986900328729326669597518287791424059647447664...
%F A071773 and gamma is the Euler-Mascheroni constant A001620. (End)
%t A071773 Table[With[{r = Apply[Times, FactorInteger[n][[All, 1]]]}, GCD[r, n/r]], {n, 104}] (* _Michael De Vlieger_, Aug 20 2017 *)
%o A071773 (PARI) a(n)=my(f=factor(n));prod(i=1,#f~,f[i,1]^(f[i,2]>1)) \\ _Charles R Greathouse IV_, Aug 08 2013
%o A071773 (Scheme)
%o A071773 ;; With memoization-macro definec.
%o A071773 (definec (A071773 n) (if (= 1 n) n (* (if (zero? (modulo n (expt (A020639 n) 2))) (A020639 n) 1) (A071773 (A028234 n))))) ;; _Antti Karttunen_, Nov 28 2017
%Y A071773 Cf. A003415, A003557, A005117, A007947, A007948, A008833, A057521, A166486 (parity of terms), A359433 (Dirichlet inverse).
%Y A071773 Cf. A065464.
%K A071773 nonn,easy,mult
%O A071773 1,4
%A A071773 _Reinhard Zumkeller_, Jun 24 2002