|
%I #16 May 19 2023 01:49:23
%S 1,2,2,4,2,4,2,8,4,4,2,8,2,4,4,8,2,8,2,8,4,4,2,16,4,4,8,8,2,8,2,16,4,
%T 4,4,16,2,4,4,16,2,8,2,8,8,4,2,16,4,8,4,8,2,16,4,16,4,4,2,16,2,4,8,32,
%U 4,8,2,8,4,8,2,32,2,4,8,8,4,8,2,16,8,4,2,16,4,4,4,16,2,16,4,8,4,4,4,32,2,8,8,16,2,8,2,16,8
%N Multiplicative with a(p^e) = 2^A007306(e).
%H Antti Karttunen, <a href="/A318316/b318316.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F a(n) = 2^A318322(n).
%F a(n) = A318307(A003557(n^2)) = A318307(A003557(n))*A318307(n).
%o (PARI)
%o A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A007306(n) = if(!n,1,A002487(n+n-1));
%o A318316(n) = factorback(apply(e -> 2^A007306(e),factor(n)[,2]));
%o (Python)
%o from functools import reduce
%o from sympy import factorint
%o def A318316(n): return 1<<sum(sum(reduce(lambda x,y:(x[0],sum(x)) if int(y) else (sum(x),x[1]),bin((e<<1)-1)[-1:2:-1],(1,0))) for e in factorint(n).values()) # _Chai Wah Wu_, May 18 2023
%Y Cf. A007306, A318307, A318322.
%K nonn,mult
%O 1,2
%A _Antti Karttunen_, Aug 31 2018
|
