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A304660
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A run-length describing inverse to A181819. The multiplicity of prime(k) in a(n) is the k-th smallest prime index of n, which is A112798(n,k).
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30
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1, 2, 4, 6, 8, 18, 16, 30, 36, 54, 32, 150, 64, 162, 108, 210, 128, 450, 256, 750, 324, 486, 512, 1470, 216, 1458, 900, 3750, 1024, 2250, 2048, 2310, 972, 4374, 648, 7350, 4096, 13122, 2916, 10290, 8192, 11250, 16384, 18750, 4500, 39366, 32768, 25410, 1296
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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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FORMULA
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a(n) = Product_{i = 1..Omega(n)} prime(i)^A112798(n,i).
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EXAMPLE
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Sequence of normalized prime multisets together with the normalized prime multisets of their images begins:
1: {} -> {}
2: {1} -> {1}
3: {2} -> {1,1}
4: {1,1} -> {1,2}
5: {3} -> {1,1,1}
6: {1,2} -> {1,2,2}
7: {4} -> {1,1,1,1}
8: {1,1,1} -> {1,2,3}
9: {2,2} -> {1,1,2,2}
10: {1,3} -> {1,2,2,2}
11: {5} -> {1,1,1,1,1}
12: {1,1,2} -> {1,2,3,3}
13: {6} -> {1,1,1,1,1,1}
14: {1,4} -> {1,2,2,2,2}
15: {2,3} -> {1,1,2,2,2}
16: {1,1,1,1} -> {1,2,3,4}
17: {7} -> {1,1,1,1,1,1,1}
18: {1,2,2} -> {1,2,2,3,3}
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MATHEMATICA
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Table[With[{y=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]}, Times@@Power[Array[Prime, Length[y]], y]], {n, 100}]
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CROSSREFS
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Cf. A055932, A056239, A112798, A130091, A133808, A181819, A181821, A182850, A182857, A275870, A304455.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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