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A060735
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a(1)=1, a(2)=2; thereafter, a(n) is the smallest number m not yet in the sequence such that every prime that divides a(n-1) also divides m.
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44
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1, 2, 4, 6, 12, 18, 24, 30, 60, 90, 120, 150, 180, 210, 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100, 2310, 4620, 6930, 9240, 11550, 13860, 16170, 18480, 20790, 23100, 25410, 27720, 30030, 60060, 90090, 120120, 150150, 180180, 210210
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OFFSET
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1,2
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COMMENTS
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Also, numbers k at which k / (phi(k) + 1) increases.
Except for the initial 1, this sequence is a primorial (A002110) followed by its multiples until the next primorial, then the multiples of that primorial and so on. - Wilfredo Lopez (chakotay147138274(AT)yahoo.com), Dec 28 2006
a(1)=1, a(2)=2. For n >= 3, a(n) is the smallest integer > a(n-1) that is divisible by every prime which divides lcm(a(1), a(2), a(3), ..., a(n)). - Leroy Quet, Feb 23 2010
Lexicographically earliest infinite sequence of distinct positive numbers with property that every prime that divides a(n-1) also divides a(n). - N. J. A. Sloane, Apr 08 2022
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LINKS
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FORMULA
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EXAMPLE
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After a(2)=2 the next term must be even, so a(3)=4.
Then a(4) must be even so a(4) = 6.
Now a(5) must be a multiple of 2*3=6, so a(5)=12.
Then a(6)=18, a(7)=24, a(8)=30.
Now a(9) must be a multiple of 2*3*5 = 30, so a(9)=60. And so on.
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MAPLE
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seq(seq(k*mul(ithprime(i), i=1..n-1), k=1..ithprime(n)-1), n=1..10); # Vladeta Jovovic, Apr 08 2004
a := proc(n) option remember; if n=1 then return 1 fi; a(n-1);
% + convert(numtheory:-factorset(%), `*`) end:
seq(a(n), n=1..42); # after Zumkeller, Peter Luschny, Aug 30 2016
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MATHEMATICA
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a = 0; Do[ b = n/(EulerPhi[ n ] + 1); If[ b > a, a = b; Print[ n ] ], {n, 1, 10^6} ]
f[n_] := Range[Prime[n + 1] - 1] Times @@ Prime@ Range@ n; Array[f, 7, 0] // Flatten (* Robert G. Wilson v, Jul 22 2015 *)
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PROG
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(PARI) first(n)=my(v=vector(n), k=1, p=1, P=1); v[1]=1; for(i=2, n, v[i]=P*k++; if(k>p && isprime(k), p=k; P=v[i]; k=1)); v \\ Charles R Greathouse IV, Jul 22 2015
(PARI) is_A060735(n, P=1)={forprime(p=2, , n>(P*=p)||return(1); n%P&&return)} \\ M. F. Hasler, Mar 14 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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