A048640 Binary encoding of the squarefree numbers, A005117.

1, 2, 4, 8, 6, 16, 10, 32, 64, 18, 12, 128, 256, 20, 34, 512, 66, 1024, 14, 2048, 36, 130, 24, 4096, 258, 68, 8192, 22, 16384, 514, 32768, 132, 65536, 40, 260, 1026, 131072, 262144, 2050, 72, 38, 524288, 516, 26, 1048576, 2097152, 4098, 48, 70, 4194304

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = 2^i1+2^i2+...+2^iz, where A005117(n) = p_i1*p_i2*p_i3*...*p_iz (p_i stands for the i-th prime, where the first prime is 2).

Example

10 = 2*5 = p_1*p_3 -> 2^1+2^3 = 2+8 = 10.

Mathematica

Total[2^PrimePi@ # &@ Map[First, FactorInteger@ #]] & /@ Select[Range@ 80, SquareFreeQ] (* Michael De Vlieger, Oct 01 2015 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (issquarefree(n), if (n==1, x = n, f = factor(n); x = sum(k=1, #f~, 2^primepi(f[k, 1]))); print1(x, ", "); ); ); } \\ Michel Marcus, Oct 01 2015

Crossrefs

Cf. A048639.

Sequence in context: A253885 A336350 A140692 * A242353 A277331 A124510

Adjacent sequences: A048637 A048638 A048639 * A048641 A048642 A048643

Keyword

nonn

Author

Antti Karttunen, Jul 14 1999

Status

approved