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%I #21 Mar 28 2021 07:01:14
%S 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,
%T 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,
%U 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
%N a(n) = A046523(A048673(n)).
%C 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.
%H Antti Karttunen, <a href="/A278224/b278224.txt">Table of n, a(n) for n = 1..10500</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F a(n) = A046523(A048673(n)).
%o (Scheme) (define (A278224 n) (A046523 (A048673 n)))
%o (Python)
%o from sympy import factorint, nextprime
%o from operator import mul
%o def P(n):
%o f = factorint(n)
%o return sorted([f[i] for i in f])
%o def a046523(n):
%o x=1
%o while True:
%o if P(n) == P(x): return x
%o else: x+=1
%o def a048673(n):
%o f = factorint(n)
%o return 1 if n==1 else (1 + reduce(mul, [nextprime(i)**f[i] for i in f]))//2
%o def a(n): return a046523(a048673(n))
%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jun 12 2017
%Y Cf. A046523, A048673, A278223.
%K nonn
%O 1,2
%A _Antti Karttunen_, Nov 16 2016
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