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Search: id:A162474
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| A162474 |
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Let b(n,p(k)) be the exponent raising the kth 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. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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If p(m) is the mth prime, then a(p(m)) = 2^(m-1).
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EXAMPLE
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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.
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MAPLE
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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) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2009]
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CROSSREFS
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Sequence in context: A100824 A163227 A048675 this_sequence A048676 A049287 A006799
Adjacent sequences: A162471 A162472 A162473 this_sequence A162475 A162476 A162477
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KEYWORD
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base,nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Jul 04 2009
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2009
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