A081211 a(n) = A081210(A081210(n)).
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, 26, 21, 29, 30, 31, 31, 33, 34, 35, 21, 37, 38, 39, 35, 41, 42, 43, 33, 35, 46, 47, 35, 47, 46, 51, 39, 53, 39, 55, 47, 57, 58, 59, 35, 61, 62, 47, 62, 65, 66, 67, 51, 69, 70, 71, 47, 73
Offset: 1
Keywords
Examples
Recall that A081210 = (in prime factorization of n: replace each prime power p^e = by the greatest squarefree number <= p^e). Consider n = 84 = 2*2*3*7, A081210(84) = 3*3*7 = 63, A081210(A081210(84)) = A081210(63) = 7*7 = 49 = a(84), A081210(A081210(A081210(84))) = A081210(A081210(63)) = A081210(49) = 47, A081212(49) = 3 as A081210(47) = 47 hence A081213(84) = 47, Therefore a(84) <> A081213(84), 49 <> 47.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
-
Maple
A081211 := proc(n) A081210(A081210(n)) ; end proc: seq(A081211(n),n=1..84) ; # R. J. Mathar, May 25 2023
-
Mathematica
gsf[n_] := For[k = n, True, k--, If[SquareFreeQ[k], Return[k]]]; A081210[n_] := Times @@ gsf /@ Power @@@ FactorInteger[n]; a[n_] := A081210[A081210[n]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Sep 12 2023 *)
-
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));} a(n) = A081210(A081210(n)); \\ Amiram Eldar, Jun 09 2025
Comments