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%I #7 Dec 21 2020 23:03:42
%S 0,1,2,3,2,3,4,5,2,3,4,5,4,5,6,7,3,4,5,6,5,6,7,8,5,6,7,8,7,8,9,10,4,5,
%T 6,7,6,7,8,9,6,7,8,9,8,9,10,11,7,8,9,10,9,10,11,12,9,10,11,12,11,12,
%U 13,14,3,4,5,6,5,6,7,8,5,6,7,8,7,8,9,10,6,7,8,9,8,9,10,11,8,9,10,11,10,11,12,13,7
%N Number of prime divisors of A339821(n), counted with multiplicity.
%H Antti Karttunen, <a href="/A339902/b339902.txt">Table of n, a(n) for n = 0..65537</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F If 4n = 2^e1 + 2^e2 + ... + 2^ek [e1 ... ek distinct], then a(n) = A023508(e1) + A023508(e2) + ... + A023508(ek).
%F a(n) = A001222(A339821(n)).
%F a(n) = A001222(A003972(A019565(n))) = A001222(A000010(A019565(2n))).
%F a(n) >= A339822(n).
%o (PARI) A339902(n) = { my(s=0, p=2); while(n>0, p = nextprime(1+p); if(n%2, s += bigomega(p-1)); n >>= 1); (s); };
%Y Cf. A000010, A001222, A003972, A019565, A023508, A339821, A339822, A339906.
%K nonn
%O 0,3
%A _Antti Karttunen_, Dec 21 2020
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