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User talk:Peter Luschny/Multifactorials

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Comments please!

'm-addorial' or 'm-termial'?

What is a good name for the additive equivalents of the m-factorials? m-addorials? Replacing 'fact' from 'factor' by 'add' from 'addend'. D. E. Knuth once used "termial" in his TAOCP. David Cantrell commented this in the MathForum:

I agree that he [Knuth] was not seriously proposing an official name, but you misread the name he used! Not "terminal", but rather "termial". Why "termial"? It's obvious. The FACTORial of n is the product of the first n positive integer FACTORs. By analogy then, Knuth calls the sum of the first n positive integer TERMs, the TERMial of n. Quaint. Let me now suggest the "obvious" postfix operation symbol for termial: Since the symbol "." is used for multiplication, and factorial is indicated by "!" (i.e. the multiplication symbol surmounted by a vertical stroke), we should analogously indicate termial by replacing the "." in "!" with "+" [..].,

Alors, 'm-addorial' or 'm-termial'? I recognize the intended meaning much easier with 'm-addorial'. However, I do not know how this sounds in the ears of a native English speaker.

Swinging patterns

Sequences of the type GCD(n!/floor(n/2)!^2, p^n): p prime, exhibit an interesting pattern. In the case p = 3 see this b-file. Is there a simple explanation of this pattern?