A338362 Inverse permutation to A283312.

1, 2, 4, 3, 6, 5, 8, 10, 11, 7, 12, 14, 15, 9, 17, 18, 19, 21, 22, 24, 25, 13, 26, 28, 29, 16, 30, 31, 32, 34, 35, 37, 38, 20, 39, 40, 41, 23, 43, 44, 45, 47, 48, 50, 51, 27, 52, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 33, 65, 67, 68, 36, 70, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82

Offset: 1

Author

N. J. A. Sloane, Nov 03 2020

Keywords

• nonn

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A283312, A338363.

Programs

Maple

g := m -> m+pi(m)-pi(m/2); #  A338363
A338362 := proc(n) global g;
if isprime(n) then return(g(n)-1); fi;
if type(n,even) then
   if isprime(n/2) then return(g(n/2)); fi;
fi;
return(g(n)); end proc;
[seq(A338362(n),n=1..128)];

Mathematica

g[n_] := n + PrimePi[n] - PrimePi[n/2];
a[n_] := Which[PrimeQ[n], g[n]-1, PrimeQ[n/2], g[n/2], True, g[n]];
Table[a[n], {n, 1, 128}] (* Jean-François Alcover, Apr 04 2023 *)

Formula

Let g(n) = A338363(n) = n + pi(n) - pi(n/2), where pi = A000720.

Then a(n) = g(n)-1 if n is a prime, a(n) = g(n/2) if n is twice a prime, and otherwise a(n) = g(n).