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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 30 12:22 EDT 2020. Contains 338079 sequences. (Running on oeis4.)