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Search: id:A037916
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| A037916 |
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Concatenate exponents in prime factorization of n. |
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+0
5
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| 0, 1, 1, 2, 1, 11, 1, 3, 2, 11, 1, 21, 1, 11, 11, 4, 1, 12, 1, 21, 11, 11, 1, 31, 2, 11, 3, 21, 1, 111, 1, 5, 11, 11, 11, 22, 1, 11, 11, 31, 1, 111, 1, 21, 21, 11, 1, 41, 2, 12, 11, 21, 1, 13, 11, 31, 11, 11, 1, 211, 1, 11, 21, 6, 11, 111, 1, 21, 11, 111, 1, 32, 1, 11, 12, 21, 11, 111
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n)=1 for prime n; a(n)=11,111,1111,... if n=product of two, three, four, ... distinct primes. Zak Seidov, Dec 15, 2006
The sequence of (nonzero) exponents in the prime factorization of a number is called its prime signature. - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 17 2008
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..2000.
Wikipedia, Prime signature.
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EXAMPLE
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12=2^2*3^1, so a(12)=21.
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PROGRAM
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(PARI) A037916(n)=if( n>1, eval(concat(concat([""], factor(n)[, 2]~)))) - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 17 2008
(PARI) primesig(n)=sum(i=1, #n=vecsort(factor(n)[, 2]), 10^(#n-i)*n[i]) \\ up to the order of digits, the same result up to 2^10. - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 17 2008
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CROSSREFS
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Sequence in context: A098290 A160110 A139393 this_sequence A143888 A016546 A141504
Adjacent sequences: A037913 A037914 A037915 this_sequence A037917 A037918 A037919
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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