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

1,2

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

Formula

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

Prog

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

Crossrefs

Cf. A046523, A048673, A278223.

Sequence in context: A286613 A229061 A339464 * A161421 A306337 A326022

Adjacent sequences: A278221 A278222 A278223 * A278225 A278226 A278227

Keyword

nonn

Author

Antti Karttunen, Nov 16 2016

Status

approved