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A369099
Index of first occurrence of n in A369015; smallest number whose prime tower factorization tree has Matula-Göbel number n.
4
1, 2, 4, 6, 16, 12, 64, 30, 36, 48, 65536, 60, 4096, 192, 144, 210, 18446744073709551616, 180, 1073741824, 240, 576, 196608, 68719476736, 420, 1296, 12288, 900, 960, 281474976710656, 720
OFFSET
1,2
COMMENTS
After a(30), the sequence continues 2^65536, 2*3*5*7*11, 2^16*3^2, 2^64*3, 2^6*3^4, 2^2*3^2*5*7, 2^60, 2^30*3, 2^12*9, 2^4*3*5*7, 2^4096, ... .
a(n) can be determined recursively as follows. Let n = Product_{i>=1} p_i^e_i, where p_i is the i-th prime. Take f_1 >= f_2 >= ... >= f_k so that the number a(i) occurs e_i times for i >= 1. Then a(n) = Product_{i>=1} p_i^f_i.
All terms are in A025487 (products of primorials).
FORMULA
a(prime(n)) = 2^a(n). As a consequence, a(A007097(n)) = A014221(n).
a(2^n) = A002110(n).
EXAMPLE
Using the method described in the comments for n = 20 = p(1)^2*p(3)^1, the exponents f_i shall include the term a(1)=1 twice and the term a(3)=4 once, i.e., (f_1, f_2, f_3) = (4, 1, 1), so a(20) = p(1)^4*p(2)^1*p(3) = 240.
PROG
(Python)
from sympy import factorint, nextprime, primepi
def A369099(n):
f = {A369099(primepi(p)):e for p, e in factorint(n).items()}
a = p = 1
for k in sorted(f, reverse=True):
for i in range(f[k]):
p = nextprime(p)
a *= p**k
return a
CROSSREFS
A permutation of A284456.
Sequence in context: A099315 A005179 A037019 * A341668 A326782 A358126
KEYWORD
nonn
AUTHOR
STATUS
approved