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A072411 LCM of exponents in prime factorization of n, a(1) = 1. 32

%I

%S 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,4,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,5,1,1,

%T 1,2,1,1,1,3,1,1,1,2,2,1,1,4,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,6,1,1,1,2,

%U 1,1,1,6,1,1,2,2,1,1,1,4,4,1,1,2,1,1,1,3,1,2,1,2,1,1,1,5,1,2,2,2,1,1,1,3,1,1,1,6,1,1,1,4,1,1,1,2,2,1,1,3

%N LCM of exponents in prime factorization of n, a(1) = 1.

%H Antti Karttunen, <a href="/A072411/b072411.txt">Table of n, a(n) for n = 1..10080</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

%F a(1) = 1; for n > 1, a(n) = lcm(A067029(n), a(A028234(n)). - _Antti Karttunen_, Aug 09 2016

%F From _Antti Karttunen_, Aug 22 2017: (Start)

%F a(n) = A284569(A156552(n)).

%F a(n) = A290103(A181819(n)).

%F a(A289625(n)) = A002322(n).

%F a(A290095(n)) = A055092(n).

%F a(A275725(n)) = A060131(n).

%F a(A260443(n)) = A277326(n).

%F a(A283477(n)) = A284002(n). (End)

%e n = 288 = 2*2*2*2*2*3*3; lcm(5,2) = 10; Product(5,2) = 10, max(5,2) = 5;

%e n = 180 = 2*2*3*3*5; lcm(2,2,1) = 2; Product(2,2,1) = 4; max(2,2,1) = 2; it deviates both from maximum of exponents (A051903, for the first time at n=72), and product of exponents (A005361, for the first time at n=36).

%e For n = 36 = 2*2*3*3 = 2^2 * 3^2 we have a(36) = lcm(2,2) = 2.

%e For n = 72 = 2*2*2*3*3 = 2^3 * 3^2 we have a(72) = lcm(2,3) = 6.

%e For n = 144 = 2^4 * 3^2 we have a(144) = lcm(2,4) = 4.

%e For n = 360 = 2^3 * 3^2 * 5^1 we have a(360) = lcm(1,2,3) = 6.

%t Table[LCM @@ Last /@ FactorInteger[n], {n, 2, 100}] (* _Ray Chandler_, Jan 24 2006 *)

%o (Scheme, with memoization-macro definec)

%o (definec (A072411 n) (if (= 1 n) 1 (lcm (A067029 n) (A072411 (A028234 n))))) ;; _Antti Karttunen_, Aug 09 2016

%o (Python)

%o from sympy import lcm, factorint

%o def a(n):

%o l=[]

%o f=factorint(n)

%o for i in f: l+=[f[i],]

%o return lcm(l)

%o print([a(n) for n in range(1, 151)]) # _Indranil Ghosh_, Mar 25 2017

%o (PARI) a(n) = lcm(factor(n)[,2]); \\ _Michel Marcus_, Mar 25 2017

%Y Cf. A028234, A067029, A072412-A072414, A273058, A284569, A290103.

%Y Similar sequences: A001222 (sum of exponents), A005361 (product), A051903 (maximal exponent), A051904 (minimal exponent), A052409 (gcd of exponents), A267115 (bitwise-and), A267116 (bitwise-or), A268387 (bitwise-xor).

%Y Cf. also A055092, A060131.

%Y Differs from A290107 for the first time at n=144.

%Y After the initial term, differs from A157754 for the first time at n=360.

%K nonn

%O 1,4

%A _Labos Elemer_, Jun 17 2002

%E a(1) = 1 prepended and the data section filled up to 120 terms by _Antti Karttunen_, Aug 09 2016

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Last modified April 19 19:31 EDT 2021. Contains 343117 sequences. (Running on oeis4.)