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

Author

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

Keywords

• nonn
• base

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

Examples

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

Crossrefs

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

Programs

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

Formula

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

Extensions

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