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 A304660 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). 21
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A permutation of A133808. a(n) is the smallest member m of A133808 such that A181819(m) = n. LINKS FORMULA a(n) = Product_{i = 1...Omega(n)} prime(i)^A112798(n,i). EXAMPLE 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} MATHEMATICA 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}] CROSSREFS Cf. A055932, A056239, A112798, A130091, A133808, A181819, A181821, A182850, A182857, A275870, A304455. Sequence in context: A326037 A100055 A334031 * A344902 A104001 A048784 Adjacent sequences:  A304657 A304658 A304659 * A304661 A304662 A304663 KEYWORD nonn AUTHOR Gus Wiseman, May 16 2018 STATUS approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)