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a(n) = A002487(A297168(n)).
1

%I #7 Feb 23 2019 07:22:41

%S 0,0,0,1,0,2,0,2,1,3,0,3,0,4,2,3,0,4,0,5,3,5,0,4,1,6,2,7,0,5,0,4,4,7,

%T 2,7,0,8,5,7,0,7,0,9,3,9,0,5,1,5,6,11,0,8,3,10,7,10,0,9,0,11,5,5,4,13,

%U 0,13,8,6,0,10,0,12,4,15,2,19,0,9,3,13,0,11,5,14,9,13,0,11,3,17,10,15,6,6,0,6,7,9,0,25,0,16,5

%N a(n) = A002487(A297168(n)).

%H Antti Karttunen, <a href="/A324285/b324285.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

%F a(n) = A002487(A297168(n)).

%o (PARI)

%o A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));

%o A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));

%o A297112(n) = if(1==n,0,2^A297167(n));

%o A297168(n) = sumdiv(n,d,(d<n)*A297112(d)); \\ _Antti Karttunen_, Feb 22 2019

%o A002487(n) = { my(s=sign(n), a=1, b=0); n = abs(n); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (s*b); };

%o A324285(n) = A002487(A297168(n));

%Y Cf. A002487, A156552, A297168.

%Y Cf. also A323902, A324115, A324116, A324049.

%K nonn

%O 1,6

%A _Antti Karttunen_, Feb 22 2019