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%I A072411 #61 Aug 20 2024 12:27:15
%S A072411 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 A072411 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 A072411 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 A072411 LCM of exponents in prime factorization of n, a(1) = 1.
%C A072411 The sums of the first 10^k terms, for k = 1, 2, ..., are 14, 168, 1779, 17959, 180665, 1808044, 18084622, 180856637, 1808585068, 18085891506, ... . Apparently, the asymptotic mean of this sequence is limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1.8085... . - _Amiram Eldar_, Sep 10 2022
%H A072411 Antti Karttunen, <a href="/A072411/b072411.txt">Table of n, a(n) for n = 1..10080</a>
%H A072411 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%H A072411 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>.
%F A072411 a(1) = 1; for n > 1, a(n) = lcm(A067029(n), a(A028234(n))). - _Antti Karttunen_, Aug 09 2016
%F A072411 From _Antti Karttunen_, Aug 22 2017: (Start)
%F A072411 a(n) = A284569(A156552(n)).
%F A072411 a(n) = A290103(A181819(n)).
%F A072411 a(A289625(n)) = A002322(n).
%F A072411 a(A290095(n)) = A055092(n).
%F A072411 a(A275725(n)) = A060131(n).
%F A072411 a(A260443(n)) = A277326(n).
%F A072411 a(A283477(n)) = A284002(n). (End)
%e A072411 n = 288 = 2*2*2*2*2*3*3; lcm(5,2) = 10; Product(5,2) = 10, max(5,2) = 5;
%e A072411 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 A072411 For n = 36 = 2*2*3*3 = 2^2 * 3^2 we have a(36) = lcm(2,2) = 2.
%e A072411 For n = 72 = 2*2*2*3*3 = 2^3 * 3^2 we have a(72) = lcm(2,3) = 6.
%e A072411 For n = 144 = 2^4 * 3^2 we have a(144) = lcm(2,4) = 4.
%e A072411 For n = 360 = 2^3 * 3^2 * 5^1 we have a(360) = lcm(1,2,3) = 6.
%t A072411 Table[LCM @@ Last /@ FactorInteger[n], {n, 2, 100}] (* _Ray Chandler_, Jan 24 2006 *)
%o A072411 (Scheme, with memoization-macro definec)
%o A072411 (definec (A072411 n) (if (= 1 n) 1 (lcm (A067029 n) (A072411 (A028234 n))))) ;; _Antti Karttunen_, Aug 09 2016
%o A072411 (Python)
%o A072411 from sympy import lcm, factorint
%o A072411 def a(n):
%o A072411     l=[]
%o A072411     f=factorint(n)
%o A072411     for i in f: l+=[f[i],]
%o A072411     return lcm(l)
%o A072411 print([a(n) for n in range(1, 151)]) # _Indranil Ghosh_, Mar 25 2017
%o A072411 (PARI) a(n) = lcm(factor(n)[,2]); \\ _Michel Marcus_, Mar 25 2017
%Y A072411 Cf. A028234, A067029, A072412-A072414, A273058, A284569, A290103.
%Y A072411 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 A072411 Cf. also A055092, A060131.
%Y A072411 Differs from A290107 for the first time at n=144.
%Y A072411 After the initial term, differs from A157754 for the first time at n=360.
%K A072411 nonn,easy
%O A072411 1,4
%A A072411 _Labos Elemer_, Jun 17 2002
%E A072411 a(1) = 1 prepended and the data section filled up to 120 terms by _Antti Karttunen_, Aug 09 2016

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