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A106491
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Total number of bases and exponents in Quetian Superfactorization of n, including the unity-exponents at the tips of branches.
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8
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1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 5, 2, 4, 4, 4, 2, 5, 2, 5, 4, 4, 2, 5, 3, 4, 3, 5, 2, 6, 2, 3, 4, 4, 4, 6, 2, 4, 4, 5, 2, 6, 2, 5, 5, 4, 2, 6, 3, 5, 4, 5, 2, 5, 4, 5, 4, 4, 2, 7, 2, 4, 5, 5, 4, 6, 2, 5, 4, 6, 2, 6, 2, 4, 5, 5, 4, 6, 2, 6, 4, 4, 2, 7, 4, 4, 4, 5, 2, 7, 4, 5, 4, 4, 4, 5, 2, 5, 5, 6, 2, 6
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OFFSET
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1,2
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LINKS
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FORMULA
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If n is a prime power p^k (a term of A000961), a(n) = 1 + a(k).
(End)
Other identities. For all n >= 1:
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EXAMPLE
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a(64) = 5, as 64 = 2^6 = 2^(2^1*3^1) and there are 5 nodes in that superfactorization. Similarly, for 360 = 2^(3^1) * 3^(2^1) * 5^1 we get a(360) = 8. See comments at A106490.
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MAPLE
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a:= proc(n) option remember; `if`(n=1, 1,
add(1+a(i[2]), i=ifactors(n)[2]))
end:
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MATHEMATICA
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PROG
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(Scheme, with memoization-macro definec)
(PARI)
A067029(n) = if(n<2, 0, factor(n)[1, 2]);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, May 09 2005 based on Leroy Quet's message ('Super-Factoring' An Integer) posted to SeqFan-mailing list on Dec 06 2003.
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STATUS
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approved
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