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A071830
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Smallest k > n such that Lpf(n) = Lpf(k) where Lpf(x) denotes the largest prime factor in x factorization.
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3
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4, 6, 8, 10, 9, 14, 16, 12, 15, 22, 18, 26, 21, 20, 32, 34, 24, 38, 25, 28, 33, 46, 27, 30, 39, 36, 35, 58, 40, 62, 64, 44, 51, 42, 48, 74, 57, 52, 45, 82, 49, 86, 55, 50, 69, 94, 54, 56, 60, 68, 65, 106, 72, 66, 63, 76, 87, 118, 75, 122, 93, 70, 128, 78, 77, 134, 85, 92
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OFFSET
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2,1
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COMMENTS
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From Rémy Sigrist, Jun 03 2017: (Start)
This sequence is a permutation of the composite numbers (A002808).
a(p) = 2*p for any prime p.
a(2^k) = 2^(k+1) for any n > 0.
For any prime p and n >= 0, a^n(p)/p is the (n+1)-th p-smooth number (where a^n denotes the n-th iterate of a).
a(n) <= 2*n for any n > 1 (as Lpf(2*n) = Lpf(n)).
See also A287932 for the least prime factor equivalent.
(End)
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 2..10000
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MATHEMATICA
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Array[Which[PrimeQ[#], 2 #, IntegerQ@ Log2[#], 2^(IntegerExponent[#, 2] + 1), True, If[#1 <= #2^2, (#1/#2 + 1) #2, Block[{k = #1/#2 + 1}, While[FactorInteger[k][[-1, 1]] > #2, k++]; k #2]] & @@ {#, FactorInteger[#][[-1, 1]]}] &[#] &, 68, 2] (* Michael De Vlieger, Nov 03 2021 *)
Lpf[x_]:=FactorInteger[x][[-1, 1]]; Array[(k=#; While[Lpf@#!=Lpf@++k]; k)&, 68, 2] (* Giorgos Kalogeropoulos, Nov 03 2021 *)
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PROG
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(PARI) for(n=2, 120, s=+1; while(abs(component(component(factor(n), 1), omega(n))-component(component(factor(n+s), 1), omega(n+s)))>0, s++); print1(n+s, ", "))
(PARI) a(n) = { my(f = factor(n)[, 1], h = f[#f], s = n\h); for(i = s+1, oo, c = factor(i)[, 1]; if(c[#c] <= h, return(i*h) ) ) } \\ David A. Corneth, Nov 03 2021
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CROSSREFS
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Cf. A002808, A006530, A287932.
Sequence in context: A161396 A145256 A087789 * A276982 A340846 A167146
Adjacent sequences: A071827 A071828 A071829 * A071831 A071832 A071833
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KEYWORD
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nonn,easy
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AUTHOR
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Benoit Cloitre, Jun 08 2002
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STATUS
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approved
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