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Search: id:A064372
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| A064372 |
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Additive function a(n) defined by the recursive formula a(1)=1 and a(p^k)=a(k) for any prime p. |
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+0
8
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| 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 2, 3
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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That is, if i, j, k, ... are relatively prime, then a(i*j*k*...) = a(i)+a(j)+a(k)+... - N. J. A. Sloane (njas(AT)research.att.com), Nov 20 2007
Starts almost the same as A001221 (the number of distinct primes dividing n): the first twelve terms which are different are a(1), a(64), a(192), a(320), a(448), a(576), a(704), a(729), a(832), a(960), a(1024) and a(1088), since the first non-unitary values of n are a(6) and(10). - Henry Bottomley (se16(AT)btinternet.com), Sep 23 2002
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
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a(n) = A106491(n)-A106490(n) = A106495(A106444(n)). - Antti Karttunen (Antti.Karttunen(AT)gmail.com), May 09 2005
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EXAMPLE
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a(30) = a(5^1 * 3^1 * 2^1) = a(1)+a(1)+a(1) = 3.
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CROSSREFS
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Cf. A001221, A079553.
Sequence in context: A087802 A079553 A001221 this_sequence A096825 A007875 A050320
Adjacent sequences: A064369 A064370 A064371 this_sequence A064373 A064374 A064375
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KEYWORD
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nonn,easy,nice
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AUTHOR
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S. R. Finch (Steven.Finch(AT)inria.fr), Sep 26 2001
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