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A357979
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Second MTF-transform of A000041. Replace prime(k) with prime(A357977(k)) in the prime factorization of n.
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6
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 31, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 59, 32, 33, 62, 35, 36, 37, 38, 39, 40, 127, 42, 79, 44, 45, 46, 47, 48, 49, 50, 93, 52, 53, 54, 55, 56, 57, 58, 211, 60, 61, 118, 63, 64, 65, 66
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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 applying a function horizontally along a number's prime indices; see the Mathematica program.
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LINKS
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EXAMPLE
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We have:
- 51 = prime(2) * prime(7),
- a(51) = prime(2) * prime(11) = 93.
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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[PartitionsP]], 100]
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CROSSREFS
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For primes instead of partition numbers we have A357983.
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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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