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A139393
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Sum( e[i] 10^(m-i), i=1..m ) where e[1]<=...<=e[m] are the nonzero exponents in the prime factorization of n: a representation of the prime signature of n.
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1
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0, 1, 1, 2, 1, 11, 1, 3, 2, 11, 1, 12, 1, 11, 11, 4, 1, 12, 1, 12, 11, 11, 1, 13, 2, 11, 3, 12, 1, 111, 1, 5, 11, 11, 11, 22, 1, 11, 11, 13, 1, 111, 1, 12, 12, 11, 1, 14, 2, 12, 11, 12, 1, 13, 11, 13, 11, 11, 1, 112, 1, 11, 12, 6, 11, 111, 1, 12, 11, 111, 1, 23, 1, 11, 12, 12, 11, 111
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The sorted sequence of (nonzero) exponents in the prime factorization of a number is called its prime signature. Here this is "approximated" by multiplying them by powers of 10. Up to 2^10 this coincides with the concatenation of these exponents written in base 10 (but that sequence would be "base" specific).
For n>=1024 one should use a modified definition, replacing 10 by 10^floor(1+log10(log2(n))), to avoid ambiguity of the representation.
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LINKS
| E. W. Weisstein, Prime signature on mathworld.wolfram.com.
Wikipedia, Prime signature.
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PROG
| (PARI) A139393(n)=sum(i=1, #n=vecsort(factor(n)[, 2]), 10^(#n-i)*n[i])
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CROSSREFS
| Cf. A037916.
Sequence in context: A054781 A098290 A160110 * A037916 A191618 A143888
Adjacent sequences: A139390 A139391 A139392 * A139394 A139395 A139396
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KEYWORD
| nonn,easy
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AUTHOR
| M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 17 2008, Apr 19 2008
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