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A065642
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a(1) = 1; for n > 1, a(n) = Min {m > n | same prime factors as n, ignoring multiplicity}.
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7
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1, 4, 9, 8, 25, 12, 49, 16, 27, 20, 121, 18, 169, 28, 45, 32, 289, 24, 361, 40, 63, 44, 529, 36, 125, 52, 81, 56, 841, 60, 961, 64, 99, 68, 175, 48, 1369, 76, 117, 50, 1681, 84, 1849, 88, 75, 92, 2209, 54, 343, 80, 153, 104, 2809, 72, 275, 98, 171, 116, 3481, 90, 3721
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A007947(a(n)) = A007947(n); a(A007947(n)) = A007947(n) * A020639(n); a(A000040(n)^k) = A000040(n)^(k+1); A001221(a(n)) = A001221(n).
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
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EXAMPLE
| a(10) = a(2 * 5) = 2 * 2 * 5 = 20; a(12) = a(2^2 * 3) = 2 * 3^2 = 18.
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MATHEMATICA
| ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] cor[x_] := Apply[Times, ba[x]] Table[Min[Flatten[Position[Table[cor[w], {w, n+1, n^2}]-cor[n], 0]]+n], {n, 1, 100}] This code is suitable since prime factor set is invariant iff squarefree kernel is invariant.
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PROG
| (Haskell)
import Data.List (find)
import Data.Maybe (fromJust)
a065642 1 = 1
a065642 n = fromJust $ find ((== sfk) . a007947) [n+1..]
where sfk = a007947 n
-- Reinhard Zumkeller, Jul 27 2011
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CROSSREFS
| Sequence in context: A063718 A063748 A121920 * A118585 A067666 A050399
Adjacent sequences: A065639 A065640 A065641 * A065643 A065644 A065645
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KEYWORD
| nice,nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 03 2001
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