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 A080087 Number of factors of 5 in the factorial of the n-th prime, counted with multiplicity. 6
 0, 0, 1, 1, 2, 2, 3, 3, 4, 6, 7, 8, 9, 9, 10, 12, 13, 14, 15, 16, 16, 18, 19, 20, 22, 24, 24, 25, 25, 26, 31, 32, 33, 33, 35, 37, 38, 39, 40, 41, 43, 44, 46, 46, 47, 47, 51, 53, 55, 55, 56, 57, 58, 62, 63, 64, 65, 66, 68, 69, 69, 71, 75, 76, 76, 77, 81, 82, 84, 84, 86, 87, 89, 90 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Highest power of 5 dividing prime(n)! = A039716(n), or also the number of trailing end 0's in A039716(n). - _Lekraj Beedassy_, Oct 31 2010 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{k=1..L} floor(prime(n)/5^k), where L = log(p_n)/log(5). a(n) = A112765(A039716(n)). - _Michel Marcus_, Sep 28 2023 MAPLE R:= NULL: v:= 0: p:= 0: for i from 1 to 100 do q:= p; p:= nextprime(p); v:= v + add(1+padic:-ordp(x, 5), x = 1+floor(q/5) .. floor(p/5)); R:= R, v; od: R; # _Robert Israel_, Sep 27 2023 MATHEMATICA lst={}; Do[p=Prime[n]; s=0; While[p>1, p=IntegerPart[p/5]; s+=p; ]; AppendTo[lst, s], {n, 5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 28 2009 *) PROG (PARI) a(n) = valuation(prime(n)!, 5); \\ _Michel Marcus_, Jan 15 2015 CROSSREFS Cf. A080084, A080085, A080086, A039716, A112765, A027868. Sequence in context: A129768 A210715 A072926 * A345163 A369728 A369986 Adjacent sequences: A080084 A080085 A080086 * A080088 A080089 A080090 KEYWORD nonn AUTHOR _Paul D. Hanna_, Jan 26 2003 STATUS approved

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Last modified February 29 23:21 EST 2024. Contains 370428 sequences. (Running on oeis4.)