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A357977
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Replace prime(k) with prime(A000041(k)) in the prime factorization of n.
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10
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1, 2, 3, 4, 5, 6, 11, 8, 9, 10, 17, 12, 31, 22, 15, 16, 47, 18, 79, 20, 33, 34, 113, 24, 25, 62, 27, 44, 181, 30, 263, 32, 51, 94, 55, 36, 389, 158, 93, 40, 547, 66, 761, 68, 45, 226, 1049, 48, 121, 50, 141, 124, 1453, 54, 85, 88, 237, 362, 1951, 60, 2659, 526
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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We have 35 = prime(3) * prime(4), so a(35) = prime(A000041(3)) * prime(A000041(4)) = prime(3) * prime(5) = 55.
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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[PartitionsP], 100]
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PROG
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(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = prime(numbpart(primepi(f[k, 1])))); factorback(f); \\ Michel Marcus, Oct 25 2022
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CROSSREFS
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Applying the same transformation again gives A357979.
Cf. A000041, A000720, A003964, A063834, A076610, A215366, A296150, A299201, A299202, A357975, 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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