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%I #20 Oct 31 2013 04:11:07
%S 6,11346,1721418,7449858,11215266,14101830,28118346,31755786,37118418,
%T 48517386,69016314,78075906,258216018,409092018,410775306,443414418,
%U 453980706,471867666,525843960,582427266,758573106,800349666,805060626,874923018,1042069218,1458081714
%N Numbers for which sum of odious proper divisors (A000069) equals sum of evil proper divisors (A001969).
%C Are there terms not divisible by 6?
%C All the displayed terms are an odd multiple of 6, and up to a few exceptions of the form a(n)=6*p*q, where p,q have the same odd Hamming weight H(p) = H(q) >= 7. - _M. F. Hasler_, Oct 27 2013
%F Common value of the considered sums of divisors is (A000203(a(n))-a(n))/2.
%e 6 has odious divisors 1,2 and proper evil divisor 3. Since 1+2=3, then 6 is in the sequence.
%o (PARI) for(n=4, 1458081714, if(isprime(n), next); nd=numdiv(n); if(nd>3, d=divisors(n); se=0; so=1; for(j=2, nd-1, if(hammingweight(d[j])%2==0, se=se+d[j], so=so+d[j])); if(se==so, print1(n ", ")))) /* _Donovan Johnson_, Oct 26 2013 */
%o (PARI) is(n,d=divisors(n))={sum(j=2, #d-1, (-1)^hammingweight(d[j])*d[j])==1} \\ - _M. F. Hasler_, Oct 27 2013
%Y Cf. A000203, A227872, A227873, A000069, A001969.
%K nonn,base
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Oct 26 2013
%E a(5)-a(26) from _Donovan Johnson_, Oct 26 2013
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