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A324922
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a(n) = unique m such that m/A003963(m) = n, where A003963 is product of prime indices.
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23
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1, 2, 6, 4, 30, 12, 28, 8, 36, 60, 330, 24, 156, 56, 180, 16, 476, 72, 152, 120, 168, 660, 828, 48, 900, 312, 216, 112, 1740, 360, 10230, 32, 1980, 952, 840, 144, 888, 304, 936, 240, 6396, 336, 2408, 1320, 1080, 1656, 8460, 96, 784, 1800, 2856, 624, 848, 432
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OFFSET
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1,2
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COMMENTS
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Every positive integer has a unique factorization into factors q(i) = prime(i)/i, i > 0 given by the rows of A324924. Then a(n) is the number obtained by encoding this factorization as a standard factorization into prime numbers (A112798).
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LINKS
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FORMULA
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a(n) = Product_t mg(t) where the product is over all (not necessarily distinct) terminal subtrees of the rooted tree with Matula-Goebel number n, and mg(t) is the Matula-Goebel number of t.
Completely multiplicative with a(prime(n)) = prime(n) * a(n). - Rémy Sigrist, Jul 18 2019
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
difac[n_]:=If[n==1, {}, With[{m=Product[Prime[i]/i, {i, primeMS[n]}]}, Sort[Join[primeMS[n], difac[n/m]]]]];
Table[Times@@Prime/@difac[n], {n, 30}]
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PROG
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(PARI) a(n) = my (f=factor(n)); prod (i=1, #f~, (f[i, 1] * a(primepi(f[i, 1])))^f[i, 2]) \\ Rémy Sigrist, Jul 18 2019
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CROSSREFS
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Sorting the sequence gives A324850.
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KEYWORD
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nonn,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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