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 A007968 Type of happy factorization of n. 12
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS 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 FORMULA a(A000290(n)) = 0; a(A007969(n)) = 1; a(A007970(n)) = 2. PROG (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 CROSSREFS Cf. A000290, A007969, A007970. Sequence in context: A339823 A127506 A353433 * A236532 A077763 A030218 Adjacent sequences: A007965 A007966 A007967 * A007969 A007970 A007971 KEYWORD nonn AUTHOR J. H. Conway STATUS approved

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Last modified September 17 10:37 EDT 2024. Contains 375987 sequences. (Running on oeis4.)