A005892: Truncated square numbers?

[N. J. A. Sloane]

Artur and SeqFans,
I've checked the book "The Little Book of Big Primes" (2nd ed.) byRibenboim, Section 2.D at page 24. It indeed states the following:
"In 1808, Legendre the exact power p^m of the prime p that divides afactorial a! (so that p^(m+1) does not divide a!)."
which seems to be consistent with the comment
%C A125552 A. M. Legendre in 1808 gave a formula for finding m.
and similar comments in other sequences (A127032, A127033, A127034,A127035, A127036, A127037, A127039). There is a problem, though.
The Legendre's formula is irrelevant to these sequences, since itindeed determines the maximum power of p *dividing* n! (as Ribenboimsaid) while Artur's sequences define the maximum power of p *notexceeding* n!.So the comments like the one quoted above should be removed from thesesequences.
P.S. As I see, Neil has already corrected these sequences according tomy previous message. That's fine but somehow "less or equal" symbol inthe sequence names got incorrectly replaced with strict < symbol.Neil, please fix it up as well.
Thanks,Max
On 1/4/07, Artur <grafix at csl.pl> wrote:> Dear Max,> I was take these title from Ribenboim book 2.2.4> ARTUR>> Dnia 04-01-2007 o 22:08:11 Max A. <maxale at gmail.com> napisał(a):>> > On 1/4/07, N. J. A. Sloane <njas at research.att.com> wrote:> >> >> Also, just to make things more difficult, Artur submitted several pairs> >> of sequences with the same A-numbers, for example:> >> %I A127030> >> %S A127030 0, 1, 2, 4, 5, 7, 9, 11, 13, 15, 18, 20, 22> >> %N A127030 Maximal value of power m such that 3^m divided n! (3^m <> >> n!)> >> > I think the name of this and other similar sequences (A127032,> > A127033, A127034, A127035, A127036, A127037, A127039) is confusing. It> > has nothing to do with the division (but rather with taking a> > logarithm), and it should be renamed to> > "Maximal value of power m such that 3^m < n!"> > with a formula> > a(n) = floor( log(n!) / log(3) ).> >> > Max>>>