Duplicate hunting, pt. 10

[Andrew Plewe]

search on the members of the sequence. If not, and it makes sense to add it,
	-Andrew Plewe-
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Subject: A074202 Numbers n such that the number of 1's in the binary representation of n divides 2^n-1.
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Date: Fri, 4 May 2007 13:13:00 -0700
From: "Joshua Zucker" <joshua.zucker at gmail.com>
To: "Andrew Plewe" <aplewe at sbcglobal.net>
Subject: Re: Duplicate hunting, pt. 10
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On 5/4/07, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> A003555 and A099639

Easy to prove that the formulas given are the same. (I don't
understand the definition of A099639, but it says "see formula below",
so I think it's OK)

> A073570 and A116964

I think there's a mistake in the formula for A116964: it says
  a(n) = SUM[d|n] (d+1)*(d+2)*(d+3)*(d+4)/24.
  a(n) = SUM[d|n] C(d,4).
  a(n) = SUM[d|n] A000332(d).

But isn't it the sum of d*(d+1)*(d+2)*(d+3)?
And then the rest have to be chanced to C(d+3,4) and A000332(d+3).

Anyway, if my corrected formula is the right formula, then these are duplicates.

> A067816 and A076629

Yes, the definitions are equivalent.

> A051538 and A119635

Looks like it should be an easy divisibility exercise to prove that
they are the same but I don't have time to do it right now :(

> A098019 and A098020

Unless e and pi are equal, it doesn't seem like these should be the
same sequence ... I have a feeling the author just pasted the wrong
set of terms into one of these.

--Joshua Zucker