cp's OEIS Frontend

A081211 a(n) = A081210(A081210(n)).

%I A081211 #23 Jun 09 2025 10:40:27
%S A081211 1,2,3,3,5,6,7,7,7,10,11,7,13,14,15,15,17,14,19,15,21,22,23,21,23,26,
%T A081211 26,21,29,30,31,31,33,34,35,21,37,38,39,35,41,42,43,33,35,46,47,35,47,
%U A081211 46,51,39,53,39,55,47,57,58,59,35,61,62,47,62,65,66,67,51,69,70,71,47,73
%N A081211 a(n) = A081210(A081210(n)).
%C A081211 a(n) = r(n,2), where r is defined as in A081212, A081213.
%C A081211 Different from A081213 (see example).
%H A081211 Reinhard Zumkeller, <a href="/A081211/b081211.txt">Table of n, a(n) for n = 1..10000</a>
%F A081211 a(n) = A081213(n) for n<84 = A131072(1); a(A131072(n)) <> A081213(A131072(n)). - _Reinhard Zumkeller_, Jun 13 2007
%e A081211 Recall that A081210 = (in prime factorization of n: replace each prime power p^e = by the greatest squarefree number <= p^e).
%e A081211 Consider n = 84 = 2*2*3*7,
%e A081211 A081210(84) = 3*3*7 = 63,
%e A081211 A081210(A081210(84)) = A081210(63) = 7*7 = 49 = a(84),
%e A081211 A081210(A081210(A081210(84))) = A081210(A081210(63)) = A081210(49) = 47,
%e A081211 A081212(49) = 3 as A081210(47) = 47 hence A081213(84) = 47,
%e A081211 Therefore a(84) <> A081213(84), 49 <> 47.
%p A081211 A081211 := proc(n)
%p A081211     A081210(A081210(n)) ;
%p A081211 end proc:
%p A081211 seq(A081211(n),n=1..84) ; # _R. J. Mathar_, May 25 2023
%t A081211 gsf[n_] := For[k = n, True, k--, If[SquareFreeQ[k], Return[k]]];
%t A081211 A081210[n_] := Times @@ gsf /@ Power @@@ FactorInteger[n];
%t A081211 a[n_] := A081210[A081210[n]];
%t A081211 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Sep 12 2023 *)
%o A081211 (PARI) A081210(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,2] == 1, f[i,1], my(k = f[i,1]^f[i,2]); while(!issquarefree(k), k--); k));}
%o A081211 a(n) = A081210(A081210(n)); \\ _Amiram Eldar_, Jun 09 2025
%Y A081211 Cf. A081210, A081213, A131072.
%K A081211 nonn
%O A081211 1,2
%A A081211 _Reinhard Zumkeller_, Mar 10 2003