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A036441
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a(n+1) = next number having largest prime dividing a(n) as a factor, with a(1) = 2.
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5
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2, 4, 6, 9, 12, 15, 20, 25, 30, 35, 42, 49, 56, 63, 70, 77, 88, 99, 110, 121, 132, 143, 156, 169, 182, 195, 208, 221, 238, 255, 272, 289, 306, 323, 342, 361, 380, 399, 418, 437, 460, 483, 506, 529, 552, 575, 598, 621, 644, 667, 696, 725, 754, 783, 812, 841, 870
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(2,n) satisfies the following inequality: 1/4*(n^2+3*n+1)<=a(n)<=1/4*(n-2)^2. Also a(a(r,k), n)=a(r,n+k-1), for all n,k in N\{0} and all r in N\{0,1}; a(prime(k), n)=a(prime(i), n+prime(k)-prime(i)), for all k,i,n e N\{0}, with k >= i, n >= prime(k-1) and with prime(x) := x-th prime.
Essentially the same as A076271.
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
| a(m, n) := a(m, n-1) + lp(a(m, n-1)), a(m, 1) := m; with lp(x) := "largest prime factor of x"
a(n) = p(m)*(n+2-p(m)), where p(k) is the k-th prime and m is the smallest index such that n+2 <= p(m) + p(m+1). [From Max Alekseyev (maxale(AT)gmail.com), Oct 21 2008]
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EXAMPLE
| a(2,2)=4 because 2+ lp(2)= 2+2=4; a(2,3)=6 because 4 + lp(4)= 4+2=6
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MATHEMATICA
| f[n_]:=Last[First/@FactorInteger[n]]; Join[{a=2}, Table[a+=f[a], {n, 2, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 08 2011*)
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PROG
| (Haskell)
a036441 n = p * (n + 2 - p) where
(p, _) = head $ dropWhile ((< n+2) . snd) $ zip a000040_list a001043_list
-- Reinhard Zumkeller, Nov 14 2011
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CROSSREFS
| Cf. A006530. See A076271 and A180107 for other versions.
Cf. A001043, A070229.
Sequence in context: A130025 A145802 A076271 * A180107 A134678 A135146
Adjacent sequences: A036438 A036439 A036440 * A036442 A036443 A036444
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KEYWORD
| eigen,nice,nonn
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AUTHOR
| Frederick Magata (fmagata(AT)smail.uni-koeln.de)
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EXTENSIONS
| Better description from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 04, 2002
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