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A309096 Increasing positive integers with prime factorization exponents all appearing earlier in the sequence. 0
1, 2, 4, 6, 12, 16, 18, 30, 36, 48, 60, 64, 90, 144, 150, 162, 180, 192, 210, 240, 300, 324, 420, 450, 576, 630, 720, 810, 900, 960, 1050, 1200, 1260, 1296, 1458, 1470, 1620, 1680, 2100, 2310, 2880, 2916, 2940, 3150, 3600, 3750, 4050, 4096, 4410, 4620, 4800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..51.

FORMULA

a(1) = 1; a(n) = least positive integer x > a(n-1) where the exponents e in the prime factorization of x are in a(1..n-1).

EXAMPLE

a(2) = 2, since 2 = 2^1 and all {1} are in a(1..1) = [1].

a(3) != 3, since 3 = 2^0 * 3^1 and not all {0,1} are in a(1..2) = [1,2].

a(3) = 4, since 4 = 2^2 and all {2} are in a(1..2) = [1,2].

a(4) != 5, since 5 = 2^0 * 3^0 * 5^1 and not all {0,1} are in a(1..3) = [1,2,4].

a(4) = 6, since 6 = 2^1 * 3^1 and all {1} are in a(1..3) = [1,2,4].

PROG

(Haskell)

wheelSeeds = [2, 3, 5, 7, 11, 13]

wheelOffsets = filter (\c -> all (\s -> mod c s /= 0) wheelSeeds) [1..product wheelSeeds]

restOfWheel = (concat (map (replicate (length wheelOffsets)) (map (* (product wheelSeeds)) [1..])))

wheel = wheelSeeds ++ (tail wheelOffsets) ++ (zipWith (+) (cycle wheelOffsets) restOfWheel)

isPrime n = and [n > 1, all (\c -> mod n c /= 0) (takeWhile (\c -> c * c <= n) wheel)]

primes = filter isPrime wheel

exponents bases acc n =

    if (n == 1)

        then (dropWhile (== 0) acc)

        else if (mod n (head bases) == 0)

            then (exponents bases (((head acc) + 1) : (tail acc)) (div n (head bases)))

            else (exponents (tail bases) (0 : acc) n)

a = filter (\n -> all (\e -> elem e (takeWhile (<= e) a)) (exponents primes [0] n)) [1..]

CROSSREFS

Sequence in context: A255001 A050584 A260698 * A019280 A090748 A188047

Adjacent sequences:  A309093 A309094 A309095 * A309097 A309098 A309099

KEYWORD

nonn

AUTHOR

Chris Murray, Jul 12 2019

STATUS

approved

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Last modified September 18 23:30 EDT 2020. Contains 337175 sequences. (Running on oeis4.)