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

6, 11346, 1721418, 7449858, 11215266, 14101830, 28118346, 31755786, 37118418, 48517386, 69016314, 78075906, 258216018, 409092018, 410775306, 443414418, 453980706, 471867666, 525843960, 582427266, 758573106, 800349666, 805060626, 874923018, 1042069218, 1458081714

Offset

1,1

Comments

Are there terms not divisible by 6?

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

Links

Table of n, a(n) for n=1..26.

Formula

Common value of the considered sums of divisors is (A000203(a(n))-a(n))/2.

Example

6 has odious divisors 1,2 and proper evil divisor 3. Since 1+2=3, then 6 is in the sequence.

Prog

(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 */
(PARI) is(n, d=divisors(n))={sum(j=2, #d-1, (-1)^hammingweight(d[j])*d[j])==1} \\ - M. F. Hasler, Oct 27 2013

Crossrefs

Cf. A000203, A227872, A227873, A000069, A001969.

Sequence in context: A069942 A261823 A146202 * A242676 A145720 A093897

Adjacent sequences: A227886 A227887 A227888 * A227890 A227891 A227892

Keyword

nonn,base

Author

Vladimir Shevelev and Peter J. C. Moses, Oct 26 2013

Extensions

a(5)-a(26) from Donovan Johnson, Oct 26 2013

Status

approved