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The least number with the prime signature of the odd part of A163511(n): a(n) = A046523(A000265(A163511(n))).
7

%I #10 Sep 03 2023 18:21:01

%S 1,1,1,2,1,4,2,2,1,8,4,4,2,6,2,2,1,16,8,8,4,12,4,4,2,12,6,6,2,6,2,2,1,

%T 32,16,16,8,24,8,8,4,36,12,12,4,12,4,4,2,24,12,12,6,30,6,6,2,12,6,6,2,

%U 6,2,2,1,64,32,32,16,48,16,16,8,72,24,24,8,24,8,8,4,72,36,36,12,60,12,12,4,36,12,12,4,12,4,4,2

%N The least number with the prime signature of the odd part of A163511(n): a(n) = A046523(A000265(A163511(n))).

%H Antti Karttunen, <a href="/A365425/b365425.txt">Table of n, a(n) for n = 0..16385</a>

%F a(n) = A336158(A163511(n)) = A046523(A064989(A163511(n))).

%F For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

%o (PARI)

%o A000265(n) = (n>>valuation(n,2));

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523

%o A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));

%o A365425(n) = A046523(A000265(A163511(n)));

%Y Cf. A000265, A046523, A064989, A163511, A336158.

%Y Cf. also A278531.

%K nonn

%O 0,4

%A _Antti Karttunen_, Sep 03 2023