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

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

Offset: 1

Author

Labos Elemer, Jun 17 2002

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

• 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.

Crossrefs

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.

Programs

Mathematica

Table[LCM @@ Last /@ FactorInteger[n], {n, 2, 100}] (* Ray Chandler, Jan 24 2006 *)

PARI

a(n) = lcm(factor(n)[,2]); \\ Michel Marcus, Mar 25 2017

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

Formula

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)

Extensions

a(1) = 1 prepended and the data section filled up to 120 terms by Antti Karttunen, Aug 09 2016