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A pernicious number is a positive integer such that the Hamming weight of its binary representation is prime.
[Wikipedia]

The meaning of ‘pernicious’:

pernicious (adj.): highly injurious or destructive, deadly
[Merriam Webster]

How did pernicious numbers end up being called that?

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    $\begingroup$ Maybe this is in the sprit of "odious" and "evil" numbers (those with an odd, resp. even number of ones in their binary representation)? $\endgroup$
    – Michael Stoll
    Commented Jan 24, 2015 at 11:41
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    $\begingroup$ Let $t(n)$ be the digit sum of the binary representation of $n$. Then Google will tell you that $n$ is called odious if $t(n)$ is odd and evil if $t(n)$ is even. Thus every number is either odious or evil, and therefore the words "odious" and "evil" cannot be pejorative in this context. It seems very likely that "pernicious" was chosen in the same spirit because it starts with the letter "p". $\endgroup$
    – Steven Landsburg
    Commented Jan 24, 2015 at 11:42
  • $\begingroup$ It looks like Michael Stoll posted while I was typing. $\endgroup$
    – Steven Landsburg
    Commented Jan 24, 2015 at 11:42
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    $\begingroup$ Since "odd" gives rise to "odious", and "even" to "evil", "prime" should really give rise to something with negative connotations beginning with "pr", not just with "p". "Primitive"? "Promiscuous"? "Privileged"? "Prevaricating"? $\endgroup$
    – Gerry Myerson
    Commented Mar 18, 2018 at 22:57

1 Answer 1

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Let $t\,(n)$ be the digit sum of the binary representation of $n$. Then Google will tell you that $n$ is called odious if $t\,(n)$ is odd and evil if $t\,(n)$ is even. Thus every number is either odious or evil, and therefore the words "odious" and "evil" cannot be pejorative in this context. It seems very likely that "pernicious" was chosen in the same spirit because it starts with the letter "p".

Full credit goes to Steven Landsburg for providing the full answer in a comment

Answer derived from his comment based on SE policy here.

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