A245447 Permutation of natural numbers: a(n) = A048673(A048673(n)).

1, 2, 3, 4, 5, 14, 8, 17, 9, 7, 6, 15, 13, 10, 38, 22, 11, 35, 23, 122, 50, 32, 18, 86, 25, 26, 138, 74, 41, 30, 12, 101, 33, 16, 43, 64, 28, 39, 24, 81, 20, 45, 68, 31, 176, 59, 63, 171, 34, 62, 203, 72, 53, 239, 44, 76, 47, 27, 19, 125, 29, 149, 218, 277, 158, 182, 113, 71, 40

Offset: 1

Author

Antti Karttunen, Jul 22 2014

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A245448.

Fixed points: A245449.

Cf. A048673, A243501, A243502.

Programs

Mathematica

b[p_?PrimeQ] := b[p] = Prime[PrimePi[p] + 1]; b[1] = 1; b[n_] := b[n] = Times @@ (b[First[#]]^Last[#]&) /@ FactorInteger[n];
A048673[n_] := (b[n] + 1)/2;
a[n_] := A048673[A048673[n]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, May 16 2017 *)

Scheme

(define (A245447 n) (A048673 (A048673 n)))

Formula

a(n) = A048673(A048673(n)).

a(n) = (1/2) * (1 + A003961((1/2) * (1+A003961(n)))). [Where A003961(n) shifts the prime factorization of n one step left.]

a(n) = ((A003961(A243501(n)/2)) + 1) / 2 = ((A003961(A243501(n))/3) + 1) / 2.

For all n >= 1, A243501(n) = A243502(a(n)).