Template:Sequence of the Day for March 31

Intended for: March 31, 2014

Timetable

• First draft entered by Charles R Greathouse IV on March 26, 2013 ✓
• Draft reviewed by Alonso del Arte on March 27, 2013 ✓ (and by Daniel Forgues on March 31, 2016 ✓)
• Draft to be approved by February 28, 2014

Yesterday's SOTD * Tomorrow's SOTD

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A214620: Numbers

n

such that at least one other integer

m

exists with the same smallest prime factor, same largest prime factor, and same set* of binary digits as

n

.

{ 18, 24, 36, 42, 48, 56, 70, 72, 84, 90, 96, 98, ... }

This sequence contains a bold conjecture: the lower natural density of this sequence is more than

1 2

. Can anyone prove or disprove this?

 ​-------------------------

* Actually, since a set is an unordered collection of distinct elements, one should say “same multiset (or bag) of binary digits as

n

.”