A162474 Let b(n,p(k)) be the exponent raising the k-th prime in the prime-factorization of n. (b(n,p(k)) may equal 0.) Write each b down in order and in binary (and exponent of zero is written as '0') with b(n,2) on the right and b(n,P) on the left, where P is the largest prime dividing n. Concatenate to form one binary number. a(n) is the decimal equivalent.

0, 1, 2, 2, 4, 3, 8, 3, 4, 5, 16, 6, 32, 9, 6, 4, 64, 5, 128, 10, 10, 17, 256, 7, 8, 33, 6, 18, 512, 7, 1024, 5, 18, 65, 12, 10, 2048, 129, 34, 11, 4096, 11, 8192, 34, 12, 257, 16384, 12, 16, 9, 66, 66, 32768, 7, 20, 19, 130, 513, 65536, 14, 131072, 1025, 20, 6, 36, 19

Offset

1,3

Comments

If p(m) is the m-th prime, then a(p(m)) = 2^(m-1).

Links

Table of n, a(n) for n=1..66.

Example

1125 has the prime-factorization, with the power of 2 on the right and power of the largest prime on the left, of 5^3 * 3^4 * 2^0. Writing down the exponents in base 2, we have 11, 100, 0. Concatenating, we have 111000, which in decimal is 56. So a(1125) = 56.

Maple

Lton := proc(L) add(op(i, L)*2^(i-1), i=1..nops(L)) ; end: A162474 := proc(n) local nred, L, p, e ; nred := n ; L := [] ; p := 2 ; while nred > 1 do e := 0 ; while nred mod p = 0 do e := e+1 ; nred := nred/p ; od: if e = 0 then L := [op(L), 0 ] ; else L := [op(L), op(convert(e, base, 2)) ] ; fi; p := nextprime(p) ; od: Lton(L) ; end: seq(A162474(n), n=1..100) ; # R. J. Mathar, Jul 30 2009

Crossrefs

Sequence in context: A174220 A334871 A048675 * A334878 A285330 A048676

Adjacent sequences: A162471 A162472 A162473 * A162475 A162476 A162477

Keyword

base,nonn

Author

Leroy Quet, Jul 04 2009

Extensions

More terms from R. J. Mathar, Jul 30 2009

Status

approved