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

1,2

Comments

a(n) = r(n,2), where r is defined as in A081212, A081213.

Different from A081213 (see example).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A081213(n) for n<84 = A131072(1); a(A131072(n)) <> A081213(A131072(n)). - Reinhard Zumkeller, Jun 13 2007

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A081210, A081213, A131072.

Sequence in context: A320034 A262882 A187043 * A081213 A081210 A285719

Adjacent sequences: A081208 A081209 A081210 * A081212 A081213 A081214

Keyword

nonn

Author

Reinhard Zumkeller, Mar 10 2003

Status

approved