login
A227889
Numbers for which sum of odious proper divisors (A000069) equals sum of evil proper divisors (A001969).
1
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
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
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
a(5)-a(26) from Donovan Johnson, Oct 26 2013
STATUS
approved