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A072411
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LCM of exponents in prime factorization of n, a(1) = 1.
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32
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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, 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, 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
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OFFSET
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1,4
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..10080
Index entries for sequences computed from exponents in factorization of n
Index entries for sequences related to lcm's
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FORMULA
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a(1) = 1; for n > 1, a(n) = lcm(A067029(n), a(A028234(n)). - Antti Karttunen, Aug 09 2016
From Antti Karttunen, Aug 22 2017: (Start)
a(n) = A284569(A156552(n)).
a(n) = A290103(A181819(n)).
a(A289625(n)) = A002322(n).
a(A290095(n)) = A055092(n).
a(A275725(n)) = A060131(n).
a(A260443(n)) = A277326(n).
a(A283477(n)) = A284002(n). (End)
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EXAMPLE
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n = 288 = 2*2*2*2*2*3*3; lcm(5,2) = 10; Product(5,2) = 10, max(5,2) = 5;
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).
For n = 36 = 2*2*3*3 = 2^2 * 3^2 we have a(36) = lcm(2,2) = 2.
For n = 72 = 2*2*2*3*3 = 2^3 * 3^2 we have a(72) = lcm(2,3) = 6.
For n = 144 = 2^4 * 3^2 we have a(144) = lcm(2,4) = 4.
For n = 360 = 2^3 * 3^2 * 5^1 we have a(360) = lcm(1,2,3) = 6.
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MATHEMATICA
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Table[LCM @@ Last /@ FactorInteger[n], {n, 2, 100}] (* Ray Chandler, Jan 24 2006 *)
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PROG
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(Scheme, with memoization-macro definec)
(definec (A072411 n) (if (= 1 n) 1 (lcm (A067029 n) (A072411 (A028234 n))))) ;; Antti Karttunen, Aug 09 2016
(Python)
from sympy import lcm, factorint
def a(n):
....l=[]
....f=factorint(n)
....for i in f: l+=[f[i], ]
....return lcm(l)
print [a(n) for n in range(1, 151)] # Indranil Ghosh, Mar 25 2017
(PARI) a(n) = lcm(factor(n)[, 2]); \\ Michel Marcus, Mar 25 2017
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CROSSREFS
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Cf. A028234, A067029, A072412-A072414, A273058, A284569, A290103.
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).
Cf. also A055092, A060131.
Differs from A290107 for the first time at n=144.
After the initial term, differs from A157754 for the first time at n=360.
Sequence in context: A051903 A324912 A157754 * A290107 A212180 A091050
Adjacent sequences: A072408 A072409 A072410 * A072412 A072413 A072414
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Jun 17 2002
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EXTENSIONS
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a(1) = 1 prepended and the data section filled up to 120 terms by Antti Karttunen, Aug 09 2016
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STATUS
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approved
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