cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A227889 Numbers for which sum of odious proper divisors (A000069) equals sum of evil proper divisors (A001969).

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%I A227889 #20 Oct 31 2013 04:11:07
%S A227889 6,11346,1721418,7449858,11215266,14101830,28118346,31755786,37118418,
%T A227889 48517386,69016314,78075906,258216018,409092018,410775306,443414418,
%U A227889 453980706,471867666,525843960,582427266,758573106,800349666,805060626,874923018,1042069218,1458081714
%N A227889 Numbers for which sum of odious proper divisors (A000069) equals sum of evil proper divisors (A001969).
%C A227889 Are there terms not divisible by 6?
%C A227889 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 A227889 Common value of the considered sums of divisors is (A000203(a(n))-a(n))/2.
%e A227889 6 has odious divisors 1,2 and proper evil divisor 3. Since 1+2=3, then 6 is in the sequence.
%o A227889 (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 A227889 (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 A227889 Cf. A000203, A227872, A227873, A000069, A001969.
%K A227889 nonn,base
%O A227889 1,1
%A A227889 _Vladimir Shevelev_ and _Peter J. C. Moses_, Oct 26 2013
%E A227889 a(5)-a(26) from _Donovan Johnson_, Oct 26 2013