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A357980
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Replace prime(k) with prime(A000720(k)) in the prime factorization of n, assuming prime(0) = 1.
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12
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1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 6, 1, 7, 4, 7, 3, 6, 5, 7, 2, 9, 5, 8, 3, 7, 6, 11, 1, 10, 7, 9, 4, 11, 7, 10, 3, 13, 6, 13, 5, 12, 7, 13, 2, 9, 9, 14, 5, 13, 8, 15, 3, 14, 7, 17, 6, 17, 11, 12, 1, 15, 10, 19, 7, 14, 9, 19, 4, 19, 11, 18, 7, 15, 10
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OFFSET
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1,3
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COMMENTS
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LINKS
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EXAMPLE
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We have 90 = prime(1) * prime(2)^2 * prime(3), so a(90) = prime(0) * prime(1)^2 * prime(2) = 12.
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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[PrimePi], 100]
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PROG
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(PARI) myprime(n) = if (n==0, 1, prime(n));
a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = myprime(primepi(primepi(f[k, 1])))); factorback(f); \\ Michel Marcus, Oct 25 2022
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CROSSREFS
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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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