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A007968
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Type of happy factorization of n.
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12
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0, 0, 1, 2, 0, 1, 1, 2, 2, 0, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 1, 1, 1, 2, 2, 0, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 0, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 0, 1, 1, 2, 2
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OFFSET
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0,4
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..300
J. H. Conway, On Happy Factorizations, J. Integer Sequences, Vol. 1, 1998, #1.
Reinhard Zumkeller, Initial Happy Factorization Data for n <= 250
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FORMULA
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a(A000290(n)) = 0; a(A007969(n)) = 1; a(A007970(n)) = 2.
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PROG
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(Haskell)
a007968 = (\(hType, _, _, _, _) -> hType) . h
h 0 = (0, 0, 0, 0, 0)
h x = if a > 0 then (0, a, a, a, a) else h' 1 divs
where a = a037213 x
divs = a027750_row x
h' r [] = h' (r + 1) divs
h' r (d:ds)
| d' > 1 && rest1 == 0 && ss == s ^ 2 = (1, d, d', r, s)
| rest2 == 0 && odd u && uu == u ^ 2 = (2, d, d', t, u)
| otherwise = h' r ds
where (ss, rest1) = divMod (d * r ^ 2 + 1) d'
(uu, rest2) = divMod (d * t ^ 2 + 2) d'
s = a000196 ss; u = a000196 uu; t = 2 * r - 1
d' = div x d
hs = map h [0..]
hCouples = map (\(_, factor1, factor2, _, _) -> (factor1, factor2)) hs
sqrtPair n = genericIndex sqrtPairs (n - 1)
sqrtPairs = map (\(_, _, _, sqrt1, sqrt2) -> (sqrt1, sqrt2)) hs
-- Reinhard Zumkeller, Oct 11 2015
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CROSSREFS
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Cf. A000290, A007969, A007970.
Sequence in context: A339823 A127506 A353433 * A236532 A077763 A030218
Adjacent sequences: A007965 A007966 A007967 * A007969 A007970 A007971
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KEYWORD
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nonn
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AUTHOR
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J. H. Conway
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STATUS
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approved
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