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Search: id:A059957
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| A059957 |
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Sum of distinct prime factors of n and n+1, or number of prime factors of n(n+1) or of LCM[n,n+1]. |
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+0
1
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| 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 4, 3, 2, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 2, 3, 4, 4, 4, 3, 3, 4, 4, 3, 4, 4, 3, 4, 4, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 4, 4, 3, 4, 4, 3, 4, 3, 3, 5, 4, 3, 4, 5, 4, 3, 3, 3, 4, 4, 4, 5, 4, 3, 3, 3, 3, 4, 5, 4, 4, 4, 3, 4, 5, 4, 4, 4, 4, 4, 3, 3, 4, 4, 3, 4, 4, 3, 5, 5
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If a(n)=2, then n is in A006549, being either a Mersenne prime, a Fermat prime minus one, or n=8, corresponding to the unique solution to Catalan's equation, 3^2 = 2^3 + 1. - Gene Ward Smith (genewardsmith(AT)gmail.com), Sep 07 2006
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FORMULA
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a(n) = A001221(A002378(n)) = A001221(n*(n+1)) = A001221(n)+A001221(n+1) because GCD[n, n+1] = 1.
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EXAMPLE
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If a(n)=2, then n is in A006549 (Mersenne-primes, Fermat-primes-1). n=30030, n has 6 prime factors, 30001=59*509 so a(30030)=6+2=8 n=30029 a(30029)=1+6=7
n=30030, n has 6 prime factors, 30001=59*509 so a(30030)=6+2=8 n=30029 a(30029)=1+6=7
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CROSSREFS
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Cf. A006549, A001221, A002378.
Sequence in context: A124064 A096916 A098014 this_sequence A165924 A094528 A077774
Adjacent sequences: A059954 A059955 A059956 this_sequence A059958 A059959 A059960
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Mar 02 2001
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