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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).
30
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
OFFSET
1,2
COMMENTS
A permutation of A133808. a(n) is the smallest member m of A133808 such that A181819(m) = n.
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 16 2018
STATUS
approved