cp's OEIS Frontend

A336158 The least number with the prime signature of the odd part of n: a(n) = A046523(A000265(n)).

%I A336158 #17 Sep 17 2022 02:01:52
%S A336158 1,1,2,1,2,2,2,1,4,2,2,2,2,2,6,1,2,4,2,2,6,2,2,2,4,2,8,2,2,6,2,1,6,2,
%T A336158 6,4,2,2,6,2,2,6,2,2,12,2,2,2,4,4,6,2,2,8,6,2,6,2,2,6,2,2,12,1,6,6,2,
%U A336158 2,6,6,2,4,2,2,12,2,6,6,2,2,16,2,2,6,6,2,6,2,2,12,6,2,6,2,6,2,2,4,12,4,2,6,2,2,30
%N A336158 The least number with the prime signature of the odd part of n: a(n) = A046523(A000265(n)).
%H A336158 Antti Karttunen, <a href="/A336158/b336158.txt">Table of n, a(n) for n = 1..65537</a>
%F A336158 a(n) = A046523(A000265(n)) = A046523(A064989(n)).
%F A336158 A000005(a(n)) = A001227(n).
%F A336158 A001221(a(n)) = A005087(n).
%F A336158 A001222(a(n)) = A087436(n).
%o A336158 (PARI)
%o A336158 A000265(n) = (n>>valuation(n,2));
%o A336158 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336158 A336158(n) = A046523(A000265(n));
%o A336158 (Python)
%o A336158 from math import prod
%o A336158 from sympy import factorint, prime
%o A336158 def A336158(n): return prod(prime(i+1)**e for i,e in enumerate(sorted(factorint(n>>(~n&n-1).bit_length()).values(),reverse=True))) # _Chai Wah Wu_, Sep 16 2022
%Y A336158 Cf. A000265, A001227, A005087, A046523, A064989, A087436, A336156, A336157, A336159, A336160.
%K A336158 nonn
%O A336158 1,3
%A A336158 _Antti Karttunen_, Jul 11 2020