cp's OEIS Frontend

A278223 Least number with the same prime signature as the n-th odd number: a(n) = A046523(2n-1).

%I A278223 #33 Sep 23 2023 12:11:52
%S A278223 1,2,2,2,4,2,2,6,2,2,6,2,4,8,2,2,6,6,2,6,2,2,12,2,4,6,2,6,6,2,2,12,6,
%T A278223 2,6,2,2,12,6,2,16,2,6,6,2,6,6,6,2,12,2,2,30,2,2,6,2,6,12,6,4,6,8,2,6,
%U A278223 2,6,24,2,2,6,6,6,12,2,2,12,6,2,6,6,2,30,2,4,12,2,12,6,2,2,6,6,6,24,2,2,30,2,2,6,6,6,12,6,2,6,6,6,6,6,2,36,2,2
%N A278223 Least number with the same prime signature as the n-th odd number: a(n) = A046523(2n-1).
%C A278223 This sequence works as a filter for sequences related to the prime factorization of odd numbers by matching to any sequence that is obtained as f(2*n - 1), 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 ..."). The last line in Crossrefs section lists such sequences that were present in the database as of Nov 11 2016, although some of the matches might be spurious.
%H A278223 Antti Karttunen, <a href="/A278223/b278223.txt">Table of n, a(n) for n = 1..32769</a>
%H A278223 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A278223 a(n) = A046523(2n - 1).
%F A278223 a(n) = A046523(A064216(n)).
%F A278223 From _Antti Karttunen_, May 31 2017: (Start)
%F A278223 a(n) = A278222(A244153(n)).
%F A278223 a(n) = A278531(A245611(n)).
%F A278223 (End)
%t A278223 a[n_] := Times @@ (Prime[Range[Length[f = FactorInteger[2*n - 1]]]]^Sort[f[[;; , 2]], Greater]); a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Jul 23 2023 *)
%o A278223 (Scheme)
%o A278223 (define (A278223 n) (A046523 (+ n n -1)))
%o A278223 (define (A278223 n) (A046523 (A064216 n)))
%o A278223 (Python)
%o A278223 from sympy import factorint
%o A278223 def P(n):
%o A278223     f = factorint(n)
%o A278223     return sorted([f[i] for i in f])
%o A278223 def a046523(n):
%o A278223     x=1
%o A278223     while True:
%o A278223         if P(n) == P(x): return x
%o A278223         else: x+=1
%o A278223 def a(n): return a046523(2*n - 1) # _Indranil Ghosh_, May 11 2017
%o A278223 (Python)
%o A278223 from math import prod
%o A278223 from sympy import prime, factorint
%o A278223 def A278223(n): return prod(prime(i+1)**e for i,e in enumerate(sorted(factorint((n<<1)-1).values(),reverse=True))) # _Chai Wah Wu_, Sep 16 2022
%Y A278223 Odd bisection of A046523.
%Y A278223 Cf. A064216, A244153, A245611, A278222, A278224, A278531.
%Y A278223 Sequences that partition or seem to partition N into same or coarser equivalence classes: A099774, A100007, A193773, A101871, A158280, A158315, A158647, A285716.
%K A278223 nonn
%O A278223 1,2
%A A278223 _Antti Karttunen_, Nov 16 2016