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a(n) = A056239(n) - A339894(n).
4

%I #7 Dec 21 2020 23:03:49

%S 0,0,0,1,0,1,0,1,1,1,0,1,0,1,1,2,0,2,0,1,1,1,0,2,2,1,2,1,0,2,0,2,1,1,

%T 2,2,0,1,1,2,0,2,0,1,2,1,0,2,2,2,1,1,0,2,2,2,1,1,0,2,0,1,2,3,2,2,0,1,

%U 1,2,0,2,0,1,2,1,2,2,0,2,3,1,0,2,2,1,1,2,0,2,2,1,1,1,2,3,0,2,2,3,0,2,0,2,2

%N a(n) = A056239(n) - A339894(n).

%H Antti Karttunen, <a href="/A339896/b339896.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>

%F a(n) = A056239(n) - A339894(n).

%F a(n) = A334201(n) - A339895(n).

%F a(n) = A339823(A122111(n)).

%o (PARI)

%o A000523(n) = if( n<1, 0, #binary(n) - 1); \\ From A000523

%o A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));

%o A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }

%o A339896(n) = (A056239(n)-A000523(A122111(n)));

%Y Cf. A000523, A056239, A122111, A334201, A339823, A339894, A339895.

%K nonn

%O 1,16

%A _Antti Karttunen_, Dec 21 2020