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%I #10 Jul 02 2018 07:25:09
%S 1,2,2,4,2,4,2,8,6,4,2,8,2,4,6,16,2,12,2,8,6,4,2,16,6,4,12,8,2,12,2,
%T 32,6,4,6,24,2,4,6,16,2,12,2,8,12,4,2,32,6,12,6,8,2,36,6,16,6,4,2,24,
%U 2,4,12,64,6,12,2,8,6,12,2,48,2,4,30,8,6,12,2,32,24,4,2,24,6,4,6,16,2,36,6,8,6,4,6,64,2,12,12,24,2,12,2,16,30,4,2,72,2
%N Filtering sequence (related to prime factorization): a(n) = A046523(A241916(n)).
%H Antti Karttunen, <a href="/A278525/b278525.txt">Table of n, a(n) for n = 1..16384</a>
%F a(n) = A046523(A241916(n)).
%F Other identities. For all n:
%F a(2^n) = 2^n.
%F a(A000040(n)) = 2.
%o (PARI)
%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A209229(n) = (n && !bitand(n,n-1));
%o A241916(n) = if(1==A209229(n), n, my(f = factor(2*n), nbf = #f~, igp = primepi(f[nbf,1]), g = f); for(i=1,nbf,g[i,1] = prime(1+igp-primepi(f[i,1]))); factorback(g)/2);
%o A278525(n) = A046523(A241916(n)); \\ _Antti Karttunen_, Jul 02 2018
%o (Scheme) (define (A278525 n) (A046523 (A241916 n)))
%Y Cf. A000040, A046523, A241916, A278220, A278221.
%K nonn
%O 1,2
%A _Antti Karttunen_, Nov 30 2016
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