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A357983
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Second MTF-transform of the primes (A000040). Replace prime(k) with prime(A064988(k)) in the prime factorization of n.
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9
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1, 2, 5, 4, 11, 10, 23, 8, 25, 22, 31, 20, 47, 46, 55, 16, 59, 50, 103, 44, 115, 62, 97, 40, 121, 94, 125, 92, 137, 110, 127, 32, 155, 118, 253, 100, 197, 206, 235, 88, 179, 230, 233, 124, 275, 194, 257, 80, 529, 242, 295, 188, 419, 250, 341, 184, 515, 274
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OFFSET
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1,2
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. We define the MTF-transform as shifting a number's prime indices along a function; see the Mathematica program.
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LINKS
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EXAMPLE
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First, we have
- 4 = prime(1) * prime(1),
- A064988(4) = prime(2) * prime(2) = 9.
- 35 = prime(3) * prime(4),
- a(35) = prime(5) * prime(9) = 253.
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
mtf[f_][n_]:=Product[If[f[i]==0, 1, Prime[f[i]]], {i, primeMS[n]}];
Array[mtf[mtf[Prime]], 100]
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CROSSREFS
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Applying the transformation only once gives A064988.
The union is A076610 (numbers whose prime indices are themselves prime).
For partition numbers instead of primes we have A357979.
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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