A322864 Permutation of nonnegative integers: a(1) = 0; for n > 1, a(n) = A122111(A156552(n)).

0, 1, 2, 4, 3, 8, 5, 16, 6, 9, 7, 32, 11, 128, 12, 18, 13, 64, 17, 256, 15, 72, 19, 512, 10, 216, 24, 54, 23, 36, 29, 2048, 192, 36864, 20, 25, 31, 36028797018963968, 120, 144, 37, 4096, 41, 524288, 48, 3136, 43, 32768, 14, 27, 360, 4294967296, 47, 1024, 21, 1048576, 61440, 128000, 53, 16384, 59, 47852207848256971424537054170092404736, 384, 100, 320, 1152, 61

Offset

1,3

Comments

Note the indexing: the domain starts from 1, but the range includes also zero.

Links

Antti Karttunen, Table of n, a(n) for n = 1..105

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

Index entries for sequences computed from indices in prime factorization

Formula

a(1) = 0; for n > 1, a(n) = A122111(A156552(n)).

For all n >= 1, a(prime(1+n)) = prime(n).

Mathematica

Table[If[n < 3, n - 1, Block[{k = #, m = 0}, Times @@ Power @@@ Table[k -= m; k = DeleteCases[k, 0]; {Prime@ Length@ k, m = Min@ k}, Length@ Union@ k]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ FactorInteger@ #] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ n]]], {n, 67}] (* Michael De Vlieger, Dec 31 2018, after JungHwan Min at A122111 *)

Prog

(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A322864(n) = if(1==n, 0, A122111(A156552(n)));

Crossrefs

Inverse permutation: A322863.

Sequence in context: A242706 A242722 A120242 * A355436 A352713 A054427

Adjacent sequences: A322861 A322862 A322863 * A322865 A322866 A322867

Keyword

nonn

Author

Antti Karttunen, Dec 30 2018

Status

approved