A278224 a(n) = A046523(A048673(n)).

1, 2, 2, 2, 4, 8, 6, 6, 2, 2, 2, 2, 4, 2, 12, 2, 6, 6, 12, 32, 12, 12, 6, 12, 4, 6, 12, 12, 16, 2, 2, 6, 6, 2, 6, 2, 6, 6, 2, 6, 6, 2, 24, 2, 24, 12, 8, 6, 2, 6, 48, 6, 30, 12, 6, 2, 6, 2, 2, 6, 6, 24, 30, 6, 60, 12, 36, 6, 2, 12, 2, 12, 24, 6, 6, 24, 72, 128, 30, 12, 2, 6, 12, 24, 2, 2, 30, 48, 4, 2, 6, 2, 6, 48, 16, 96, 6, 30, 2, 6, 12, 6, 24, 30, 2, 2, 6

Offset: 1

Author

Antti Karttunen, Nov 16 2016

Keywords

• nonn

Comments

This sequence works as a "sentinel" for sequence A048673 by matching to any other sequence that is obtained as f(A048673(n)), where f(n) is any function that depends only on the prime signature of n (see the index entry for "sequences computed from exponents in ..."). As of Nov 11 2016 no such sequences were present in the database.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10500
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A046523, A048673, A278223.

Programs

Python

from sympy import factorint, nextprime
from operator import mul
def P(n):
    f = factorint(n)
    return sorted([f[i] for i in f])
def a046523(n):
    x=1
    while True:
        if P(n) == P(x): return x
        else: x+=1
def a048673(n):
    f = factorint(n)
    return 1 if n==1 else (1 + reduce(mul, [nextprime(i)**f[i] for i in f]))//2
def a(n): return a046523(a048673(n))
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 12 2017

Scheme

(define (A278224 n) (A046523 (A048673 n)))

Formula

a(n) = A046523(A048673(n)).