

A162474


Let b(n,p(k)) be the exponent raising the kth prime in the primefactorization 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.


1



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
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OFFSET

1,3


COMMENTS

If p(m) is the mth prime, then a(p(m)) = 2^(m1).


LINKS

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


EXAMPLE

1125 has the primefactorization, 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^(i1), 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



